When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 60.0-kg man just before contact with the ground has a speed of 4.18 m/s. (a) In a stiff-legged landing he comes to a halt in 1.00 ms. Find the magnitude of the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.245 s. Find the magnitude of the average net force now. (c) During the landing, the force of the ground on the man points upward, while the force due to gravity points downward. The average net force acting on the man includes both of these forces. Taking into account the directions of the forces, find the magnitude of the force applied by the ground on the man in part (b).
Answers
Answer:
a) The average force that acts on the man is \(2.508\times 10^{8}\) newtons.
b) The average force that acts on the man is 1023.673 newtons.
c) The force of the ground on the man is 1612.093 newtons upwards.
Explanation:
a) After a careful reading of the statement we construct the following model by applying Impact Theorem, that is:
\(m\cdot \vec v_{A} + \vec F \cdot \Delta t = m\cdot \vec v_{B}\) (Eq. 1)
Where:
\(m\) - Mass of the man, measured in kilograms.
\(\vec v_{A}\) - Initial velocity of the man, measured in meters per second.
\(\vec v_{B}\) - Final velocity of the man, measured in meters per second.
\(\Delta t\) - Impact time, measured in seconds.
\(\vec F\) - Average net force, measured in newtons.
Now we proceed to clear average net force within expression:
\(\vec F \cdot \Delta t = m\cdot (\vec v_{B}-\vec v_{A})\)
\(\vec F = \frac{m}{\Delta t}\cdot (\vec v_{B}-\vec v_{A})\) (Eq. 2)
If we know that \(m = 60\,kg\), \(\vec v_{A} = -4.18\,\hat{j}\,\,\,\left[\frac{m}{s} \right]\), \(\vec v_{B} = 0\,\hat{j}\,\,\,\left[\frac{m}{s} \right]\) and \(\Delta t = 1\times 10^{-6}\,s\), we obtain the following vector:
\(\vec F = \frac{60\,kg}{1\times 10^{-6}\,s} \cdot (4.18\,\hat{j})\,\,\,\left[\frac{m}{s} \right]\)
\(\vec F = 2.508\times 10^{8}\,\hat{j}\,\,\,[N]\)
The average force that acts on the man is \(2.508\times 10^{8}\) newtons.
(b) If we know that \(m = 60\,kg\), \(\vec v_{A} = -4.18\,\hat{j}\,\,\,\left[\frac{m}{s} \right]\), \(\vec v_{B} = 0\,\hat{j}\,\,\,\left[\frac{m}{s} \right]\) and \(\Delta t = 0.245\,s\), we obtain the following vector:
\(\vec F = \frac{60\,kg}{0.245\,s} \cdot (4.18\,\hat{j})\,\,\,\left[\frac{m}{s} \right]\)
\(\vec F = 1023.673\,\hat{j}\,\,\,\left[N\right]\)
The average force that acts on the man is 1023.673 newtons.
(c) From Second Newton's Law we find the following equation of equilibrium:
\(\vec F = \vec N -\vec W\) (Eq. 3)
Where:
\(\vec F\) - Average force that acts on the man, measured in newtons.
\(\vec N\) - Force of the ground on the man, measured in newtons.
\(\vec W\) - Weight of the man, measured in newtons.
By applying the concept of weight, we expand the previous equation:
\(\vec F = \vec N -m\cdot \vec g\) (Eq. 3b)
Where \(\vec g\) is the gravitational acceleration, measured in meters per square second.
And then we clear the force of the ground on the man:
\(\vec N = \vec F +m\cdot \vec g\) (Eq. 4)
If we get that \(\vec F = 1023.673\,\hat{j}\,\,\,\left[N\right]\), \(m = 60\,kg\) and \(\vec g = 9.807\,\hat{j}\,\,\,\left[\frac{m}{s^{2}} \right]\), the average force is:
\(\vec N = 1023.673\,\hat{j}\,\,\,[N]+(60\,kg)\cdot (9.807\,\hat{j})\,\,\,\left[\frac{m}{s^{2}} \right]\)
\(\vec N = 1612.093\,\hat{j}\,\,\,\left[N\right]\)
The force of the ground on the man is 1612.093 newtons upwards.
Related Questions
An 11-kilogram cart is pulled with a horizontal force at a constant velocity of 8.0 meters per second, as shown in the diagram. The force of friction between the cart and the floor is 12 newtons. What is the magnitude of the horizontal force?
Answers
The cart is in equilibrium since it's moving at a constant velocity. This means the net horizontal force on the cart is 0, so the frictional force and pulling force cancel one another. So the pulling force has magnitude 12 N, same as the frictional force.
The refractive indices of materials A and B have a ratio of nA/nab=1,33. The speed of light in material A is 1.25 times 10^8m/s. What is the speed of light in material B?
Answers
The speed of light in material B is 1.6625 × 108 m/s.
The refractive index of a material is its optical density relative to that of a vacuum.
Material B has a refractive index of nB, and its speed of light is vB.
The speed of light in material A is given as 1.25 x 108 m/s.
The refractive indices of materials A and B have a ratio of nA/nB = 1.33.
We will use the formula:
nA/nB = vB/vA = nA/nB.
Therefore, nA/nB = vB/1.25 x 108 m/s.
This equation can be rearranged to give the speed of light in material B:
vB = nA/nB × 1.25 x 108 m/s.
Therefore, vB = 1.33 × 1.25 × 108 m/s.
We will perform this calculation:
vB = 1.6625 × 108 m/s.
Therefore, the speed of light in material B is 1.6625 × 108 m/s.
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An inductor of 247 mH with a resistance of 37 Ω is connected to a power supply with a maximum voltage of 336 V and a frequency of 71 Hz. Find the current in the circuit. Answer in units of A. 022 (part 2 of 3) 10.0 points Find the phase angle between the current and applied voltage. Answer in units of ◦ . 023 (part 3 of 3) 10.0 points Find the power loss in the inductor. Answer in units of W.
Answers
Answer:
(i) The current in the circuit is 2.044 A
(ii) the phase angle is 71.441⁰
(iii) The power loss in the inductor is 154.58 W
Explanation:
Given;
inductance, L = 247 mH
resistance, R = 37 Ω
maximum voltage, V₀ = 336 V
frequency, f = 71 Hz
The rms voltage is given as;
\(V_{rms} = 0.7071V_o\\\\V_{rms} = 0.7071 \ \times \ 336\\\\V_{rms} = 237.586 \ V\\\)
The inductive reactance is given as;
\(X_l = \omega \ L\\\\X_l = 2\pi f L\\\\X_l = 2\pi (71)(247 \times 10^{-3})\\\\X_l = 110.202 \ ohms\)
The impedance of the A.C circuit is given as;
\(Z = \sqrt{X_l^2 + R^2} \\\\Z = \sqrt{(110.202)^2 + (37)^2}\\\\Z = 116.248 \ ohms\)
(i) The current in the circuit is given as;
\(I_{rms} = \frac{V_{rms}}{Z}\\\\ I_{rms} =\frac{237.586}{116.248} \\\\I_{rms} =2.044 \ A\)
(ii) the phase angle is given as;
\(tan \phi = \frac{X_l}{R}\\\\tan \phi =\frac{110.202}{37} \\\\ tan \phi =2.9784\\\\\phi = tan^{-1} (2.9784)\\\\\phi = 71.441 ^0 \\\\\)
(iii) The power loss in the inductor is given as;
P = IVcosΦ
P = (2.044)(237.586)Cos(71.441⁰)
P = 154.58 W
Which property of a substance can be determined using a pH indicator?
O acidity
OB. boiling point
Oc density
OD. electrical conductivity
OE. thermal conductivity
Answers
Answer:
Acidity
Explanation:
pH measures how acidic or basic a substance is.
Answer:
a) Acidity
More to know The pH scale is a mixture of indicator which on dissolving indicate whether the substances is acidic in nature or basic . The value between 1 to 7 is acidic The value between 7 to 14 is basic The value 7 is neutralAcids are sour in taste and turn blue litmus ( indicator) to red Base are bitter in taste and turn red litmus to blue. Salts are neutral and obtain by the reaction between acid and bases.Một chất điểm chuyển động trong mặt phẳng Oxy với phương trình :
{ = 2 + 10
Answers
Answer:
plz write your questions in English
3. A car with a mass of 1600 kg has a kinetic energy of 125 000 J. How fast is it moving?
Answers
The car is moving at approximately 12.5 meters per second.
The kinetic energy (KE) of an object can be calculated using the formula:
KE = 1/2 * m * \(v^2\)
where
KE = kinetic energy,
m =Mass of the object, and
v = velocity.
In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .
Substituting the values , we have:
125,000 J = 1/2 * 1600 kg *\(v^2\)
Now, we can solve for v by rearranging the equation:
\(v^2\) = (2 * 125,000 J) / 1600 kg
\(v^2\) = 156.25 \(m^2/s^2\)
Taking the square root, we find:
v = √156.25\(m^2/s^2\)
v ≈ 12.5 m/s
Therefore, the car is moving at approximately 12.5 meters per second.
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A racing car traveling with constant increases its speed from 10 m/s; 30 m/s over a distance of 60 mlong does this take? to
Answers
Answer:
Explanation:
constant acceleration???
assume it to be so
average speed is (10 + 30) / 2 = 20 m/s
t = d/v = 60/20 = 3 s
Which individual or group had perhaps the most profound effect on establishing social work as a specialized practice
Answers
Answer:
Which individual or group had perhaps the most profound effect on establishing social work as a specialized practice
Explanation:
A box of mass 210 kg is pulled from rest with a string of tension 1300n inclined at 35° to the horizontal. if the box moved with a speed of 10m/s and frictional force between the box and surface is 100 n, calculate the distance covered.
Answers
If A box of mass 210 kg is pulled from rest with a string of tension 1300n inclined at 35° to the horizontal. if the box moved with a speed of 10m/s and the frictional force between the box and surface is 100 n, Then the distance covered by the box is 10.89 meters.
To calculate the distance covered by the box, we need to analyze the forces acting on it and apply the work-energy principle.
Given:
Mass of the box, m = 210 kg
Tension in the string, T = 1300 N
The angle of inclination, θ = 35°
Frictional force, f = 100 N
Initial speed, u = 0 m/s
Final speed, v = 10 m/s
First, let's resolve the tension force into components parallel and perpendicular to the incline. The parallel component of the tension force can be calculated as:
T_parallel = T * cos(θ)
Next, let's calculate the net force acting on the box along the incline. The net force is given by:
Net force = T_parallel - f
Now, using Newton's second law, we can calculate the acceleration (a) of the box:
Net force = m * a
From the given information, we have the final velocity (v), initial velocity (u), and acceleration (a). We can use the following kinematic equation to calculate the distance covered (s):
v^2 = u^2 + 2as
Rearranging the equation, we get:
s = (v^2 - u^2) / (2a)
Now, let's plug in the given values and calculate the distance covered:
T_parallel = 1300 N * cos(35°) ≈ 1067.35 N
Net force = 1067.35 N - 100 N = 967.35 N
a = (967.35 N) / (210 kg) ≈ 4.61 m/s^2
s = (10 m/s)^2 - (0 m/s)^2 / (2 * 4.61 m/s^2) ≈ 10.89 m
Therefore, the distance covered by the box is approximately 10.89 meters.
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Free association and dream analysis are techniques used in psychoanalysis to discover a person’s unconscious urges.
Please select the best answer from the choices provided
True or False?
Answers
Answer:
T on edge
Explanation:
Answer:
true
Explanation:
Identifying Sources of Error in the Experiment Which factors could be potential sources of error in the experiment? Check all that apply. energy lost in the lever due to friction color of the soda bottle used in the experiment visual estimation of height of the beanbag temperature of the lab at the time of the experiment position of the fulcrum for the lever affecting transfer of energy?
Answers
The color of the soda bottle used in the experiment and temperature of the lab at the time of the experiment are not likely to have a significant impact on the outcome of the experiment.
What is Energy?
Energy is a fundamental concept in physics that refers to the ability of a system to perform work. It can be defined as the capacity of a physical system to do work or produce heat. Energy can exist in many different forms, such as mechanical, thermal, electromagnetic, and chemical energy. It can be transferred between objects or converted from one form to another, but it cannot be created or destroyed. The SI unit of energy is the joule (J), but other units such as kilowatt-hours (kWh) and calories (cal) are also commonly used.
Energy lost in the lever due to friction, visual estimation of height of the beanbag, and position of the fulcrum for the lever affecting transfer of energy could be potential sources of error in the experiment.
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A baseball player swings his bat with hisarms fully extended. If hisarms are pulled in closer to the body, and he swings again, which of the following is true aboutthe angular momentum and kinetic energy of the player?
Angular Momentum Kinetic Energy
(A) Increases Increases
(B) Increases Remains Constant
(C) Remains Constant Increases
(D) Remains Constant Remains Constant
(E) Decreases Remains Constant
Answers
Answer:
(D) Remains Constant Remains Constant
Explanation:
Taking a swing with his arms closer to his body does not change the angular momentum or kinetic energy of this player.
The angular momentum is constant or stays the same if an object is spinning, except there is an external torque which acts on it. Also the kinetic energy stays constant as long as magnitude still remains the same and the only thing that is changing here is direction
A girl with a mass of 32 kg is playing on a swing. There are three main forces
acting on her at any time: gravity, force due to centripetal acceleration, and
the tension in the swing's chain (ignore the effects of air resistance). At the
instant shown in the image below, she is at the bottom of the swing and is
traveling at a constant speed of 4 m/s. What is the tension in the swing's
chain at this time? (Recall that g = 9.8 m/s²)
Tension
Weight
A. 333.6 N
OB. 817.8 N
C. 562.8 N
D. 441.6 N
4 m/s
Answers
The tension in the swing's chain at the instant shown in the image is 441.6 N.
option D
What is the tension at bottom swing?At the bottom of the swing, the girl is traveling at a constant speed, so her acceleration is zero. Therefore, the net force acting on her is also zero.
Thus, we have:
0 = T - mg - mv²/r
where;
T is the tension in the swing's chain, m is the girl's mass, g is the acceleration due to gravity, v is her speed, and r is the radius of the swing.At the bottom of the swing, the radius is equal to the length of the chain, so we have:
r = L = 4.0 m
Substituting the values we have:
T = (32 kg)(9.8 m/s²) + (32 kg)(4 m/s)²/4.0 m
Solving for T, we get:
T = (32 kg)(9.8 m/s²) + (32 kg)(4 m/s)²/4.0 m
T = 441.6 N.
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Have you heard of the world Karma before, what do you think it means?
Answers
Hopes it helps you.
Answer:
I think karma means anytime you mess someone up like hit them on purpose later on if you life you gonna get hit worse
Explanation:
A certain CD has a playing time of 74.0 minutes. When the music starts, the CD is rotating at an angular speed of 480 revolutions per minute (rpm). At the end of the music, the CD is rotating at 210 rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s2.
Answers
Answer: \(0.00636\ rad/s^2\)
Explanation:
Given
CD has a playing time of \(t=74\ min\ or\ 74\times 60\ s\)
Initial angular speed of CD is \(480\ rpm\)
Final angular speed of DC is \(210\ rpm\)
Angular speed, when rpm is given
\(\omega =\dfrac{2\pi N}{60}\)
\(\omega_i=\dfrac{2\pi \times 480}{60}\\\\\Rightarrow \omega_i=16\pi \ rad/s\)
Final speed
\(\Rightarrow \omega_f=\dfrac{2\pi \times 210}{60}\\\\\Rightarrow \omega_f=7\pi \ rad/s\)
Using equation of angular motion
\(\Rightarrow \omega_f=\omega_i+\alpha t\)
Insert the values
\(\Rightarrow 7\pi =16\pi +\alpha \times 74\times 60\\\Rightarrow -9\pi =\alpha \cdot (4440)\\\\\Rightarrow \alpha=-\dfrac{9\pi}{4440}\\\\\Rightarrow \alpha=-0.00636\ rad/s^2\)
Magnitude of angular acceleration is \(0.00636\ rad/s^2\)
..............................
Answers
A highly optimized power plant is designed for burning natural gas at 1100 degrees Celsius for its gas turbines which will be combined with a steam power plant for producing steam at 700 degrees Celsius using the combustion products exhausted from the gas turbine. The steam power plant will use cooling towers (i.e. the ambient air at 27 degrees Celsius) for its condensing units. The efficiency of the plant is claimed to be 78%. Evaluate this claim and comment.
Answers
The claimed efficiency of the power plant is 78%, which is significantly higher than the theoretical maximum efficiency of 29.2%. Further information is required to evaluate the claim.
The greatest conceivable proficiency of the consolidated cycle power plant can be determined involving the Carnot productivity recipe as follows:
η_Carnot = (1373 K - 973 K)/1373 K = 29.2%
This implies that the hypothetical greatest proficiency of the power plant is 29.2%.
The guaranteed proficiency of the power plant is 78%. This is fundamentally higher than the hypothetical most extreme proficiency of 29.2%, which recommends that the case isn't precise. There might be different elements that are adding to the guaranteed effectiveness, like the utilization of further developed innovation, yet minus any additional data, assessing the claim is troublesome.
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Star A has a magnitude of 1.0 and is 60 times brighter than B. What is magnitude of B?
Answers
Answer:
The magnitude scale used in astronomy is logarithmic, meaning that each increase in magnitude represents a decrease in brightness by a factor of approximately 2.512. Therefore, if Star A has a magnitude of 1.0 and is 60 times brighter than Star B, we can calculate the magnitude of Star B as follows:
Brightness ratio = 2.512^(magnitude difference)
60 = 2.512^(magnitude of A - magnitude of B)
Taking the logarithm base 2.512 of both sides:
log base 2.512(60) = magnitude of A - magnitude of B
Solving for the magnitude of B:
magnitude of B = magnitude of A - log base 2.512(60)
magnitude of B = 1.0 - log base 2.512(60)
Calculating the value:
magnitude of B ≈ 1.0 - 2.799
magnitude of B ≈ -1.799
Therefore, the magnitude of Star B is approximately -1.799.
Explanation:
Using the magnitude equation, we deduced that given star A has a magnitude of 1.0 and is 60 times brighter than star B, the magnitude of star B comes out to be approximately 4.4. This computation confirms that the larger the magnitude, the fainter the star.
Explanation:To find the magnitude of star B given that star A is 60 times brighter, we first need to understand the concept of magnitude in astronomy. In general, in the magnitude system, each difference of 1 in magnitude corresponds to a difference in brightness by a factor of about 2.512 (which is the fifth root of 100). This is represented in the equation m2 = m1 - 2.5 log(b2/b1), where m1 and m2 are the magnitudes of the two stars, and b1 and b2 are their brightness levels.
Given that star A has a magnitude of 1.0 (m1) and is 60 times brighter than star B (b2/b1), we can plug these values into the equation to get m2 = 1.0 - 2.5 log(1/60). Solving this equation, star B's magnitude comes out to be approximately 4.4. Hence, it is evident from this calculation that a larger magnitude signifies a fainter star, which aligns with the core concept of the magnitude scale in astronomy.
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The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.40 the weight of the object is 4.2
Answers
The frictional force of an object is the product of the normal force and coefficient of kinetic friction. Here the frictional force acting on the object is 16.4 N.
What is frictional force?
Frictional force is a kind of force acting on a body to resist it from motion. Thus, the direction of the force will be in negative with the magnitude. Frictional force is the product of coefficient of friction and the normal force.
The normal force acting on the object of mass 4.2 Kg is N = mg
N = 4.2 Kg × 9.8 m/s² = 41.16 N
Frictional force = ц N
= 0.40 × 41.16 N
= 16.4 N.
Therefore, the frictional force acting between the surface of the object and the floor is 16.4 N
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Your question is incomplete. But your complete question probably was:
The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.40 the weight of the object is 4.2 kg. What is the frictional force of the object?
According to the article, what was the effect of elevation on the experimental group?
Answers
Answer:
Due to the effect of elevation on the experimental group the participants decided to try to help the research assistant who was having opening one of her files to finish the study. Schnall, Roper, and Fessler were able to conclude that happiness associated with a feeling of elevation can lead to more altruism or helping behaviors.
Explanation:
100 percent on edge
The effect of elevation on the experimental group was they show more urge of being altruistic and feeling happiness and satisfaction associated with elevation.
Altruism:
It is a practice in which a person help others without any selfishness, the person just want to help.
Witnessing someone's altruistic behavior, make other to feel good and a urge of being Altruistic, this is known as elevation.
After watching elevating Oprah video, the test group help the research assistant who was having trouble in opening file.
Therefore, the effect of elevation on the experimental group was they show more urge of being altruistic and feeling happiness and satisfaction associated with elevation.
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If you are driving 80 km/h along a straight road and you look to the side for 1.7 s , how far do you travel during this inattentive period?
Express your answer using two significant figures.
Answers
Given the speed of the driver and the time elapsed, distance traveled during his inattentive period is 0.037 kilometers.
How far did the driver travel during the inattentive period?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Speed = 80 km/hTime = 1.7sDistance travelled = ?First, convert 1.7 seconds to hours.
Time = 1.7s = (1.7 / (60×60)hr = 1.7/3600 hrs
Now, find the distance traveled during the inattentive period.
80 km/h = Distance ÷ 1.7/3600 hrs
Distance = 80 km/h × 1.7/3600 hrs
Distance = 136/3600 km
Distance = 0.037 km.
Given the speed of the driver and the time elapsed, distance traveled during his inattentive period is 0.037 kilometers.
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Two spherical balls are placed so that their centers are 3.61 m apart. The
force between them is 1.65 x 10-7 N. If the mass of the smaller ball is 81 kg,
what is the mass in kilograms of the other ball?
Answers
Answer:
The mass of the other ball is 397.775 kg.
Explanation:
Gravitation is the force of mutual attraction that bodies experience due to the fact that they have a certain mass.
The universal law of gravitation is a classical physical law that describes the gravitational interaction between different bodies with mass.
The law was formulated by Newton, who deduced that the force with which two bodies of different masses are attracted only depends on the value of their masses and the square of the distance that separates them.
In other words, the Law of Universal Gravitation predicts that the force exerted between two bodies of masses M1 and M2 separated by a distance "d" is proportional to the product of their masses and inversely proportional to the square of the distance, that is:
\(F=G\frac{M1*M2}{d^{2} }\)
where:
F = It is the module of the force exerted between both bodies, and its direction is found on the axis that joins both bodies. G = It is the constant of Universal Gravitation, whose value is 6.67384*10⁻¹¹ \(\frac{N*m^{2} }{kg^{2} }\)In this case:
F= 1.65*10⁻⁷ NG= 6.67384*10⁻¹¹ \(\frac{N*m^{2} }{kg^{2} }\)M1= 81 kgM2= ?d= 3.61 mReplacing:
\(1.65*10^{-7} N=6.67384*10^{-11} \frac{N*m^{2} }{kg^{2} }\frac{81 kg*M2}{(3.61 m)^{2} }\)
Solving for M2:
\(M2=\frac{1.65*10^{-7} N*(3.61 m)^{2}}{6.67384*10^{-11} \frac{N*m^{2} }{kg^{2} }*81 kg}\)
M2= 397.775 kg
The mass of the other ball is 397.775 kg.
A rigid body is rotating with constant angular speed 3 radians per second about a fixed axis through the points A. (4, 1, 1), B. (2, -1; 0), distances being measured in centimeters. The rotation is in the left-handed sense relative to the direction AB
1, Determine the unit vector pointing in the direction BA.
2, What is the angular velocity () of the of the body?
3, Write the position vector of point P: P .
Find the instantaneous velocity of particle P [hint v = w×r)
4, What is meant by left-handed rotation (left-handed coordinate system)?
5, Write the position vectors of points A and B The rotation axis AB has direction BA. Write the direction BA in terms of the components given above.
Answers
1.Unit vector in the direction BA: BA/|BA| = (2/3, 2/3, 1/3)
2.The angular velocity (ω) of the body is given as 3 radians per second.
3.Without the position of point P given, it is not possible to write the position vector of P.
4.Left-handed rotation refers to the direction of rotation where the rotation follows the left-hand rule.
5.Position vector of point A: (4, 1, 1)
Position vector of point B: (2, -1, 0)
The direction vector BA = (-2, -2, -1)
1.To determine the unit vector pointing in the direction BA, we subtract the coordinates of point B from the coordinates of point A and normalize the resulting vector.
The direction vector BA is given by:
BA = (4 - 2, 1 - (-1), 1 - 0) = (2, 2, 1)
To obtain the unit vector in the direction of BA, we divide the direction vector by its magnitude:
|BA| = √(2^2 + 2^2 + 1^2) = √(4 + 4 + 1) = √9 = 3
Unit vector in the direction BA: BA/|BA| = (2/3, 2/3, 1/3)
2.The angular velocity (ω) of the body is given as 3 radians per second.
3.Without the position of point P given, it is not possible to write the position vector of P. Please provide the position of point P to proceed with the calculation.
4.Left-handed rotation refers to the direction of rotation where the rotation follows the left-hand rule. In a left-handed coordinate system, if you curl the fingers of your left hand in the direction of rotation, your thumb will point in the direction of the rotation axis. It is the opposite direction to a right-handed rotation.
5.The position vectors of points A and B are:
Position vector of point A: (4, 1, 1)
Position vector of point B: (2, -1, 0)
The direction vector BA can be obtained by subtracting the coordinates of point A from the coordinates of point B:
BA = (2 - 4, -1 - 1, 0 - 1) = (-2, -2, -1)
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The motion of particles in solids, liquids, and gases are distinct in their behavior. Which state of matter is randomly separated with no regular arrangement and move freely at high speeds?
A. Solid
B.Liquid
C.Mixture
D.Gas
Answers
Answer:
D. Gas
Explanation:
There are only three states of matter: solid, liquid and gas. This makes choice c (Mixture) incorrect because it is not part of the group.
The particles in gas are widely separated, which means there's a lot of free space between the particles. This makes it easily compressible. The particles then move past each other, which causes no regular arrangement.
Help me please,
A ball is thrown straight up in the air. What is the velocity and acceleration at the top of the path?
A) v 0m/s, = 0m/s/s
B) v = 0m/s, a 10m/s/s
C) v = 10m/s, a 10m/s/s
D) v = 10m/s, a = 0m/s/s
E) None of the above
Answers
Option B
Explanation:
no distance was given only the acceleration due to the fact that it went up (10m/s/s)
s0 it is
0 m/s and 10m/s/s (option B)
Question 8 of 10 A scientist adds different amounts of salt to 5 bottles of water. She then measures how long it takes for the water to boil. What is the responding variable in this experiment? A. The brand of salt used B. The time it takes for the water to boil C. The kind of bottles used D. The amount of salt added to the water SUBMIT it's B
Answers
Answer:
Explanation:
A scientist adds different amounts of salt to 5 bottles of water. She then measures how long it takes for the water to boil. What is the responding variable in this experiment? A. The time it takes for the water to boil B. The amount of salt added to the water C. The kind of bottles used D. The brand of salt used
suppose you pluck a string on a guitar and it produces the note a at a frequency of 440 hz h z . now you press your finger down on the string against one of the frets, making this point the new end of the string. the newly shortened string has 4/5 the length of the full string. part a when you pluck the string, what will its frequency be? when you pluck the string, what will its frequency be? 352 hz h z 440 hz h z 528 hz h z 550 hz h z
Answers
The frequency of the newly shortened string will be option (d) 550 Hz.
When you press your finger down on the string against one of the frets, you are effectively changing the length of the string and therefore changing its resonant frequency. The new frequency can be calculated using the following formula:
f = (1/2L) × sqrt(T/μ)
where:
f is the resonant frequency (in Hz)
L is the length of the string (in meters)
T is the tension on the string (in newtons)
μ is the linear mass density of the string (in kg/m)
In this case, the length of the newly shortened string is 4/5 of the full string, so L' = (4/5)L. The tension and linear mass density of the string remain the same.
Plugging these values into the formula, we get:
f' = (1/2L') × sqrt(T/μ) = (1/2 × 4/5L) × sqrt(T/μ) = (2/5L) × sqrt(T/μ)
Now we need to plug in the given values for the full string frequency (f) and solve for the new frequency (f'):
f = 440 Hz
L = length of full string
L' = (4/5)L
f' = (2/5L) × sqrt(T/μ)
Using the fact that the frequency is inversely proportional to the length of the string, we can solve for L:
f/f' = L/L'
L = (f/f') × L'
L = (440 Hz) / (f') × (4/5L)
L = (440 Hz × 5L) / (4f')
Solving for f', we get:
f' = (440 Hz × 5L) / (4L)
f' = (440 Hz × 5) / 4
f' = 550 Hz
Therefore, the correct option is (d) 550 Hz
Learn more about resonant frequency here
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if a car begins at rest and accelerates to 60 mph with an average acceleration of 13.5 m/her/sec. how much time will it take to get to 60 mph?
Answers
Answer:
Explanation:
First, we need to convert the velocity to meters per second:
60 mph = 88.5 ft/s = 26.82 m/s
Now we can use the formula:
v = at
where v is the final velocity, a is the acceleration, and t is the time.
Rearranging this formula, we get:
t = v/a
Substituting the values, we get:
t = 26.82 m/s / 13.5 m/s^2 = 1.987 seconds (rounded to three decimal places)
Therefore, it will take approximately 1.987 seconds to reach 60 mph with an average acceleration of 13.5 m/her/sec.
The vehicle will hit 60 mph in 7152 seconds (or about 1 hour and 59 minutes) with an average acceleration of 13.5 m/hr/sec.
What is acceleration ?The definition of acceleration is. The pace at which velocity changes with regard to time. Because it has both amount and direction, acceleration is a vector variable. It is also the second derivative of location in relation to time, or the first derivative of motion in relation to time.
We can begin by converting the final velocity to meters per second (m/s) as the initial acceleration is given in m/hr/sec.
60 mph = 26.8224 m/s (1 mile = 1.60934 km, 1 hour = 3600 seconds)
Now, we can use the formula:
v = u + at
Where,
v = final velocity = 26.8224 m/s
u = initial velocity = 0 m/s (car starts at rest)
a = acceleration = 13.5 m/hr/sec = 0.00375 m/s^2 (convert from m/hr/sec to m/s^2)
t = time taken to reach the final velocity
Substituting the values, we get:
26.8224 = 0 + (0.00375)t
t = 26.8224 / 0.00375
t ≈ 7152 seconds
learn more about acceleration
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An 12.000 milligram particle is sliding across a friction-less one-dimensional path at 55.000 m/s and collides with a 68.000 milligram particle moving at -48.000 m/s in a perfectly inelastic collision. What are the velocities of the particles after the collision?
answer with correct units
Answers
Answer:
-3525.000 m/s
Explanation:
In a perfectly inelastic collision, the two particles stick together and move with a common velocity after the collision. We can use the conservation of momentum to solve for this common velocity.
The initial momentum of the system is:
p_initial = m1 * v1 + m2 * v2
= (12.000 mg)(55.000 m/s) + (68.000 mg)(-48.000 m/s)
= -282.000 kg·m/s
Here, we convert the masses to kilograms to match the units of velocity.
Since the particles stick together after the collision, their masses add up:
m_final = m1 + m2
= 12.000 mg + 68.000 mg
= 80.000 mg
= 0.080 g
Now, we can use the conservation of momentum to find the final velocity:
p_final = m_final * v_final
where p_final = p_initial and m_final = 0.080 g.
Therefore:
v_final = p_final / m_final
= -282.000 kg·m/s / 0.080 g
= -3525.000 m/s
Draw a free body diagram of an 6.4 kg ball falling towards earth. Calculate the weight of the ball.
Answers
Diagram:-
\(\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines\put(3,6){\circle{3}}\put(2.9,4.5){\vector(0,-3){2cm}}\put(-3.9,-10){\line(3,0){3cm}}\multiput(-3.5,-10)(0.8,0){18}{\line(1,-2){2mm}}\put(-3.7,0){$\sf\footnotesize 9.8 ms^{-2}$}\put(6,0){\vector(0,3){1.2cm}}\put(5.5,6){\line(3,0){2mm}}\put(5,-1.2){\sf\footnotesize height}\put(6,-2){\vector(0,-3){1.2cm}}\put(5.5,-8){\line(1,0){2mm}}\end{picture}\)
Here
m=6.4kg\(\\ \sf\longmapsto Weight=mg\)
\(\\ \sf\longmapsto Weight=6.4(9.8)\)
\(\\ \sf\longmapsto weight=62.72N\)