How will you make a 200 ml solution of 5 mm sucrose from a 100 mm sucrose solution?
Answers
To make a 200 ml solution of 5 mm sucrose from a 100 mm sucrose solution we have to take a volume of: 10ml of the concentrated solution
To solve this problem, the formula and the procedure that we have to use is:
c1 * v1 = c2 * v2
Where:
c1= concentration of the concentrated solutionv1 = volume of the concentrated solutionc2 = concentration of the diluted solutionv2 = volume of the diluted solutionInformation about the problem:
c1 = 100 mmv1=?c2 = 5 mmv2=200 mlApplying the dissolution of concentrations formula and clearing the volume of the concentrated solution (c1) we get:
c1 * v1 = c2 * v2
v1 = (c2 * v2)/ c1
v1 = (5 mm * 200 ml)/ 100 mm
v1= 10 ml
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Related Questions
(PLS HELP!!!) Which best describes the ecosystem of a lake or pond?
A.
They are aquatic because they are made of land.
B.
They are aquatic because they are made of water.
C.
They are terrestrial because they are made of land.
D.
They are terrestrial because they are made of water.
Answers
Answer: B.
Explanation:
Lakes and ponds are considered aquatic regions, as almost all life in them is marine.
If F = 4.0 N and m = 2.0 kg, what is the magnitude a of the acceleration for the block shown below? The surface is frictionless. *
Answers
The magnitude of the acceleration of the block is 3.5 \(\bold{m/s^2.}\)
The correct option is (C) 3.5 \(\bold{m/s^2.}\)
What do you mean by acceleration?Acceleration is the rate of change of velocity with time.
By Newton’s Second law
This law establishes the relationship between the net applied force on an object with the resultant acceleration. For a constant magnitude of force, the more is the mass of the object, the lesser will be its acceleration.
Given,
The mass of the block is 2.0 kg.
The force in the horizontal direction on the block is \(\bold{4.0 N + 4.0 N \cos 40{}^\circ.}\)
a is the acceleration in the horizontal direction.
The acceleration for the block can be determined using Newton’s Second law,
\(\begin{aligned} \Sigma F&=ma \\ F+F\cos 40{}^\circ &=ma \\ a&=\frac{F\left( 1+\cos 40{}^\circ \right)}{m} \\ &=\frac{4.0\text{ N}\left( 1.766 \right)}{2.0\text{ kg}} \\ &=3.5\text{ m/}{{\text{s}}^{2}} \end{aligned}\)
Thus, the acceleration is 3.5 \(\bold{m/s^2.}\)
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I only need 25. What is the skiers kinetic energy at point B? Hint mechanical energy equals potential energy plus kinetic energy
Answers
Difference in height = 10 - 5 = 5 meters
Kinetic energy = Energy ( 500 N) x height (5 m) = 2,500 N/m = 2,500 joules
Answer: 2,500 joules
When fabricating a 90°-bend, the distance to the bending mark is equal to? Select one: a. The height of the desired stub-up b. The stub-up minus the take-up c. The take-up minus the stub-up d. The leg length plus the stub length
Answers
The distance to the bending mark when fabricating a 90°-bend is equal to the stub-up minus the take-up. Therefore, the correct answer is option b.
When bending a conduit or pipe to create a 90° angle, the bending mark represents the point at which the bend starts. The stub-up is the length of the conduit that extends vertically from the bottom of the bend to the end of the conduit. The take-up is a measurement that accounts for the additional length of the conduit that is consumed during the bending process.
To find the distance to the bending mark, you need to subtract the take-up from the desired stub-up length. This will give you the correct position to mark on the conduit before starting the bending process. Following this guideline will help ensure that your 90°-bend will be accurate and meet the required specifications.
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Please help. A weight is pulled up with a spring such that the spring force is equal to 35N and the weight accelerates upwards at 3m/s^2 solve for the mass of the weight
Answers
Force = mass × acceleration
Now, keeping this formula in mind you can find the mass as follows;
= 35 = m × 3
= 35/3 = m
= 11.6 kg = m
And yeah its done!:)
An object moving with uniform acceleration has a velocity of 11.0 cm/s in the positive x-direction when its x-coordinate is 2.76 cm. If its x-coordinate 2.25 s later is −5.00 cm, what is its acceleration?
Answers
Given:
The initial velocity is
\(v_i=\text{ 11 cm/s}\)The initial position is x1 = 2.76 cm
The final position is x2 = - 5 cm
The time will be t = 2.25 s
To find the acceleration.
Explanation:
The acceleration can be calculated by the formula
\(\begin{gathered} \Delta x=v_it+\frac{1}{2}at^2 \\ \frac{1}{2}at^2=\Delta x-v_it \\ a=\frac{2(\Delta x-v_it)}{t^2} \end{gathered}\)Here, the displacement is
\(\begin{gathered} \Delta x=x2-x1 \\ =-5-2.76 \\ =-7.76\text{ cm} \end{gathered}\)On substituting the values, the acceleration will be
\(\begin{gathered} a=\frac{2(-7.76-11\times2.25)}{(2.25)^2} \\ =\text{ -12.84 cm/s}^2 \end{gathered}\)Final Answer: The acceleration is -12.84 cm/s^2
Which of the following is an example of a biotic factor depending on an abiotic factor?
a
Fish depending on water for a habitat and for oxygen.
b
Rabbits depending on grass for food.
c
Lions depending on gazelle for food.
d
Trees depending on fungi to break down dead things in the soil.
Answers
Answer:
The correct answer is B. Algae and fungi are biotic; temperature and rainfall are abiotic.. FURTHER EXPLANATION. An ecosystem consists of all living and non-living factors in an environment that interact and that are interdependent with each other.. All living things or factors in an ecosystem are called biotic factors.Examples include organisms like plants, animals, humans, etc.
Explanation:
three swimmers who all swim at the same speed discuss how to cross a river in the shortest amount of time. swimmer a will swim straight across the river at a right angle to the current. swimmer b reasons that the current will carry a downstream, meaning that a will cover a greater distance to get across and therefore will take a longer time interval. b says he will aim at an upstream angle such that, allowing for the current, he will reach the other side directly across from where he starts, thus covering the shortest distance and arriving first. swimmer c , reasoning that the time interval needed for b to cross will be longer than b expects because some of b 's effort will be spent battling the current, plans to aim at a downstream angle, so that the current assists rather than opposes him. this way he will be traveling at the highest speed and get across first. part a which swimmer gets across first? which swimmer gets across first? swimmer a gets across first. all swimmers get across at the same time. swimmer b gets across first. swimmer c gets across first. request answer provide feedback
Answers
Swimmer C gets across first. The reasoning behind the three swimmers crossing the river is different. Swimmer A swims directly across the river. Swimmer B swims upstream at an angle that allows him to be carried downstream by the current and reach the other side directly across from his starting point.
Swimmer C swims downstream at an angle that allows him to be carried downstream by the current, therefore, making the current work for him. Therefore, Swimmer C gets across first because he is swimming at the highest speed due to the help of the current. Swimmer B will take longer than he expects because some of his efforts will be spent battling the current. Swimmer A will cover the longest distance and will take longer than both Swimmer B and Swimmer C. Hence, Swimmer C is the one who gets across first.
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it is possible for an excited hydrogen atom to return to the ground state by the emission of a single photon. regardless of the initial excited state, this electron transition produces a spectral line in which region of the electromagnetic spectrum?
1. ultraviolet
2. infrared
3. visible light
4. radio waves
Answers
Answer:
1. Ultraviolet
Explanation:
This is called the Balmer series. Transitions ending in the ground state (n = 1) are called the Lyman series, but the energies released are so large that the spectral lines are all in the ultraviolet region of the spectrum.
It is possible for an excited hydrogen atom to return to the ground state by the emission of a single photon. Regardless of the initial excited state, this electron transition produces a spectral line in ultraviolet region of the electromagnetic spectrum. The correct option is 1.
What is electromagnetic spectrum?An electromagnetic spectrum is the spectrum consisting of the colors of radiation of a white light with different wavelengths.
It is possible for an excited hydrogen atom to return to the ground state by the emission of a single photon.
The transitions which ends in the ground state (n = 1) are termed as Lyman series. Energy released is large in amount so that the spectral lines fall in the ultraviolet region of the spectrum.
Thus, regardless of the initial excited state, this electron transition produces a spectral line in ultraviolet region of the electromagnetic spectrum. The correct option is 1.
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This is an earth science question about Issac Newton’s laws and I need some major help
Answers
the 2-lb brick slides down a smooth roof, such that when it is at a it has a velocity of 5 ft/s.
Answers
The unstretched length so that it does not allow the block to leave the surface until θ= 60° is L = 4.574 ft.
Given:
The weight of the block W = 2 lb
The initial velocity of the block v_i = 0
The stiffness of the spring k = 2 lb/ft
The radius of the cylindrical surface r = 2 ft
Compute the velocity of the block at θ= 60°. Use Newton's second equation of motion in direction normal to the surface.
= F_n = m X a_n
Where, a_n is the centripetal acceleration or normal component of acceleration as follows:
= a_n = v²_2 / r
Substitute:
= F_n = m*v²2 / r
Where, F_n normal force acting on block by the surface is:
= F_n = W X cos(θ)
Substitute:
W*cos(θ) = m*v^2_2 / r
v_2 = sqrt ( r*g*cos(θ) )
Plug in the values:
v²_2 = 2 X 32.2 X cos(60)
v²_2 = 32.2 (ft/s)²
Apply the conservation of energy between points A and B where θ= 60° :
T_A + V_A = T_B + V_B
Where,
T_A : Kinetic energy of the block at initial position = 0
V_A: potential energy of the block initial position
V_A = 0.5 X k X x_A²
x_A = 2 X π- L ( L is the original length )
V_A = 0.5X 2 X (2 X πi - L)² =
= (2 X pi - L)²
T_B = 0.5 X W/g X v_2² =
= 0.5 X 2 / 32.2 X 32.2 = 1
V_B = 0.5 X k X x_B² + W X 2 X cos(60)
and, x_B = 2 X 0.75 X π - L ( L is the original length )
V_B = 0.5 X 2 X (1.5 X π - L)² + 2 X 1
= 2 + ( 1.5 X π- L )²
Input the respective energies back in to the conservation expression:
= 0 + (2π - L)² = 1 + 2 + ( 1.5π - L )²
= 4π² - 4πL + L² = 3 + 2.25π² - 3πL + L²
= πL = 1.75π² - 3
= L = 4.574 ft
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The complete question;
the 2-lb brick slides down a smooth roof, such that when it is at a it has a velocity of 5 ft/s. The 2-lb block is released from rest at A and slides down along the smooth cylindrical surface. Of the attached spring has a stiffness k = 2 lb/ft. Determine its unstretched length so that it does not allow the block to leave the surface until θ= 60°.
The order of convergence for finding one of the roots of function f(x) = x²-3x²+4 using Newton's Raphson method is (Hint: P=2) A) α = 1 B) α = 2 C) α = 3 D) α = 4
Answers
The order of convergence for finding one of the roots of the function `f(x) = x²-3x²+4` using Newton's Raphson method is `α = 2`. The correct option is (B) α = 2.
Explanation:Given that the function is `f(x) = x²-3x²+4`To find the root of the function using Newton's Raphson method is, `x(n+1) = x(n) - f(x(n))/f'(x(n))`where `x(n+1)` is the new estimate and `x(n)` is the old estimate.Now, `f(x) = x²-3x²+4`Differentiate w.r.t x to get, `f'(x) = 2x - 6x = -4x`Thus, the iteration formula becomes: `x(n+1) = x(n) - (x²(n) - 3x(n)² + 4)/-4x(n)`Simplify to obtain, `x(n+1) = x(n) + (x(n)² - 3x(n)² + 4)/4x(n)`Further simplification results in `x(n+1) = (3x(n)² - 4)/4x(n)`To find the order of convergence, the formula for `p` is used. `p = (lim n->∞) (x(n+1) - L)/(x(n) - L)^α`where `L` is the actual root of the equation.Since `f(x) = x²-3x²+4`, then `f'(x) = 2x - 6x = -4x`Therefore, `x(n+1) = x(n) - (x²(n) - 3x(n)² + 4)/-4x(n)`x(0) = 1 is the initial approximation.x(1) = 2.25x(2) = 1.9475x(3) = 1.9337x(4) = 1.9337We observe that after x(2), the values repeat themselves and do not move any further. Hence `L = 1.9337`.Then, `p = (lim n->∞) (x(n+1) - L)/(x(n) - L)^α`Taking logarithms of both sides, we have: `log|xn+1 - L| = αlog|xn - L| + log K`where `K` is a constant value on the interval `n = 0, 1, 2, 3...`Hence the order of convergence is given as `α = 2`.Therefore, the correct option is (B) α = 2.
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4. The distance s travelled by a particle depends partly on the initial velocity u and time tand partly also on the acceleration a and tim e t. Establish a relationship between the four quantities.
Answers
The greater the acceleration, the greater the velocity and the shorter the time.
Hope this helps :)
Answer:
S = V0 t + 1/2 a t^2 standard equation
Where S is the distance traveled and V0 the initial speed
At first, right after the Big Bang, the universe was too hot for nuclei and electrons to combine into the kinds of neutral atoms that are familiar to us today. How soon after the beginning did it become cool enough for neutral atoms to form
Answers
After the Big Bang, it took the universe 3 minutes to become cool enough for neutral atoms to form.
Time taken for the universe to cool after the Big Bang
During the first moment, immediately after the Big Bang, the universe was too hot for nuclei and electrons to combine into the kinds of neutral atoms that are familiar to us today.
In the first three minutes after the Big Bang, these protons and neutrons began fusing together, forming deuterium also known as heavy hydrogen.
Thus, after the Big Bang, it took the universe 3 minutes to become cool enough for neutral atoms to form.
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the diagram shows a basic hydraulic system which has a small piston and a large piston with cross-sectional areas of 0.005m² and 0.1m² respectively. A force of 20 N is applied to the small piston. Determine (a) the pressure transmitted in the hydraulic fluid (b) the mass of the load
Answers
The pressure transmitted in the hydraulic fluid is 4000 Pa and the mass of the load is 40.82 kg.
To determine the pressure transmitted in the hydraulic fluid, we can use the formula:
Pressure = Force / Area
Given that a force of 20 N is applied to the small piston and the cross-sectional area of the small piston is 0.005 m², we can calculate the pressure as follows:
Pressure = 20 N / 0.005 m²
Pressure = 4000 Pa
Therefore, the pressure transmitted in the hydraulic fluid is 4000 Pa.
To determine the mass of the load, we need to consider the equilibrium of forces in the hydraulic system. The force applied to the small piston is transmitted to the larger piston. Since the system is in equilibrium, the force exerted by the larger piston must balance the force applied to the small piston.
Using the formula:
Force = Pressure × Area
The force exerted by the larger piston can be calculated as follows:
Force = Pressure × Area (large piston)
Force = 4000 Pa × 0.1 m²
Force = 400 N
Therefore, the force exerted by the larger piston is 400 N.
Since force is equal to mass multiplied by acceleration (F = m × a), and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the mass of the load:
400 N = mass × 9.8 m/s²
Solving for the mass:
mass = 400 N / 9.8 m/s²
mass ≈ 40.82 kg
Therefore, the mass of the load is approximately 40.82 kg.
The question was incomplete. find the full content below:
The diagram shows a basic hydraulic system which has a small piston and a large piston with cross-sectional areas of 0.005m² and 0.1m² respectively. A force of 20 N is applied to the small piston. Determine (a) the pressure transmitted in the hydraulic fluid (b) the mass of the load
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A machine launches a tennis ball at an angle of 45° with the horizontal, as
shown. The ball has an initial vertical velocity of 9.0 meters per second and an initial
horizontal velocity of 9.0 meters per second. The ball reaches its maximum height
0.p2 second after its launch. [Neglect air resistance and assume the ball lands at the
same height above the ground from which it was launched.]
Elapsed Time
+0.92 s
Viy = 9.0 m/s
Launcher
V = 9.0 m/s
45
Horizontal
The total horizontal distance traveled by the tennis ball during the entire time it is in the air is
Answers
The motion or path of the tennis ball is the path of a projectile, which has
both vertical and horizontal motion.
The total horizontal distance traveled by the tennis ball during the entire
time it is in the air ≈ 16.514 meters.
Reasons:
The given parameters are;
The direction in which the ball is launched = 45°
The initial vertical velocity of the ball, \(v_y\) = 9.0 m/s
The initial horizontal velocity of the ball, vₓ = 9.0 m/s
The time it takes the ball to reach the maximum height, t = 0.92 seconds after its launch
The total horizontal distance traveled, by the tennis ball is given by the formula;
\(\Delta d_x = \dfrac{v_1^2 \cdot \left( 2 \cdot cos(\theta) \sin(\theta)}{y} = \dfrac{2 \times v_x \times v_y}{g}\)
Which gives;
\(\mathrm{The \ total \ distance \ travelled, \ \Delta} d_x = \dfrac{2 \times 9.0\times 9.0}{9.81} \approx 16.514\)
The total horizontal distance traveled by the tennis ≈ 16.514 meters
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Which of the following graphs have the same wavelengths?
Answers
Calculate the velocity of an object thrown straight up with an initial velocity of 25 m/s at 1.0 seconds.
Answers
Answer:
15 m/s
Explanation:
Given:
v₀ = 25 m/s
a = -10 m/s²
t = 1.0 s
Find: v
v = at + v₀
v = (-10 m/s²) (1.0 s) + 25 m/s
v = 15 m/s
17. For how long should a force of 130 N be applied to an object of mass 50 kg to change its speed from 20 m/s to 60 m/s?
a. 0.031 s
b. 0.065 s
c. 15.4 s
d. 40 s
Answers
Answer:
c. 15.4 s
Explanation:
Given the following data;
Mass, m = 50kg
Force, F = 130N
Initial velocity, u = 20m/s
Final velocity, v = 60m/s
To find the time;
First of all, we would solve for acceleration using the formula below;
Force = mass * acceleration
130 = 50*acceleration
Acceleration = 130/50
Acceleration = 2.6m/s²
Now, we would use the first equation of motion to find the time.
V = U + at
60 = 20 + 2.6t
2.6t = 60 - 20
2.6t = 40
t = 40/2.6
Time, t = 15.39 ≈ 15.4 seconds.
The time taken will be 15.4 seconds approximately. The correct answer is option c
NEWTON SECOND LAW
Newton's second law state that, the rate of change of momentum is proportional to the force applied.
Given that a force of 130 N be applied to an object of mass 50 kg to change its speed from 20 m/s to 60 m/s. The given parameters are;
Force F = 130 Nmass m = 50 kgInitial velocity u = 20 m/sFinal velocity V = 60 m/sfrom Newton's second law,
Ft = m(v - u)
Substitute all the parameters into the formula
130t = 50 (60 - 20)
130t = 50 x 40
130t = 2000
t = 2000/130
t = 15.38 seconds
Therefore, the time taken will be 15.4 seconds approximately. The correct answer is option c
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A Chromebook is accelerated out a widow at 8m/s/s. How much force was needed for this acceleration?
Answers
A Chromebook is accelerated out a widow at 8m/s². The amount of force was needed for this acceleration is (F)=10.88 N
What is acceleration?When a object start with a velocity and end with other velocity, The difference of velocity divided by given time is called the acceleration. This is a vector quantity.
How can we calculate the force?To calculate the force we are using the formula here is,
F=ma
Here we are given,
m= The mass of the Chromebook we know = 1.36 kg.
a = The acceleration of the object = 8 m/s².
We have to calculate the value of force = F
Now we put the values in the equation we get,
F=ma
Or, F = 1.36*8
Or, F=10.88N
From the above calculation we can say that, The amount of force was needed for this acceleration is (F)=10.88 N
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Answer: The amount of force needed for the acceleration is F=10.88N
Explanation:
what is acceleration?acceleration is the rate of change of velocity over time, both in terms of speed and direction. It is a vector quantity.
what is force?A mass-containing object's change in velocity is referred to as a force when a push or pull is applied to it. A body can change its state of rest or motion when an external force acts on it. It is directed and has a magnitude.
How do we calculate force?using formula, F=ma
where, F=force ; m=mass ; a= acceleration
given quantities are:
known mass(m) of Chromebook= 1.36kg
acceleration (a)= 8m/s²
on putting the values in the formula we get,
F=ma
F=1.36*8
F=10.88N
therefore amount of force needed for this acceleration of 8m/s² is 10.88N
Additional knowledgevelocity:It defines the direction in which the body or item is moving. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
speed:Speed is the rate of movement of an object along a path in time.
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6. What is chemical reactivity?
Answers
Answer:
What is chemical reactivity?Chemical reactivity is therefore usually predictable, based on the chemicals involved and the circumstances of them mixing.Chemical reactivity can provide a certain qualitative insight into aromaticity. ❁❀Thank you❀❁identify the necessary parts to build a calorimeter.
Answers
Answer:
Metal cans.
Food sample.
Scale.
Cork.
Paper clip.
Graduated cylinder, flask, or other container to measure water.
Thermometer.
Implement to punch holes in can.
Explanation:
S_I_L_
_O_T_A_L
P_W_R
J_M_
S_E_D_
_A_S_N_
K_C_
Answers
Answer:
Football
Power
Jamm
Steady
Kick
Newton’s law of universal gravitation is given by 2 F GMm r Where F is the gravitational force, M and m are masses, and r is a length. Derive the SI unit of the proportionality constant G? Note: Force is has the SI unit kgm/s2 (Newton).
Answers
The SI unit of the proportionality constant G is given as
[G] = [M]^3 / [Kg s²]
What is Newton’s law of universal gravitation?Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
We substitute [kg]=[M], [m]=[L], and [F]-[kg x m] / [s²]- [M] [L]/ [T²]
into
Newton's law of universal gravitation to obtain
[M][L] [G][M] [T [CF
Solving for [C] then gives
m³
[G] = [L]^3 / [M][T]² kg
[G] = [M]^3 / [Kg s²]
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If the ice extended right around the earth, forming a loop that that puck could go around in circles would the puck keep going forever?
Answers
If the ice extended right around the earth, forming a loop that the puck could go around in circles, the puck would not keep going forever. The laws of physics would eventually cause the puck to come to a stop. This is because of two factors: air resistance and gravity.
Air resistance is the force that opposes the motion of objects through the air. It is what causes things like parachutes to slow down as they fall. Even if there were no air in the hypothetical scenario of a loop of ice around the earth, there would still be air resistance. This is because the puck would be moving through the magnetic field of the earth, which would create a force that would oppose its motion.Gravity is the force that pulls objects towards each other. It is what keeps us on the ground and the planets in orbit around the sun. In the hypothetical scenario of a loop of ice around the earth, the puck would be subject to the gravitational pull of the earth. As it traveled around the loop, it would lose kinetic energy due to this gravitational force. Eventually, it would come to a stop at the bottom of the loop, where the force of gravity would be the strongest.The speed at which the puck would come to a stop would depend on a number of factors, including the size of the loop, the mass of the puck, and the force of gravity. However, in general, it is safe to say that the puck would not keep going forever if it were to travel around a loop of ice around the earth.For such more question on motion
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An object in free fall has a velocity of 5 m/s in the upward direction. What is the instantaneous velocity of the object one second later?
Answers
An object in free fall near the Earth's surface has an acceleration due to gravity of 9.8 m/s² downward. If the object has an initial velocity of 5 m/s upward, it will continue to move upward for a while before gravity pulls it back down.
One second later, the object will have been under the influence of gravity for one more second. During this time, its upward velocity will have decreased by 9.8 m/s² due to the acceleration of gravity, making it zero at the highest point of its trajectory.
As the object continues to fall, its downward velocity will increase by 9.8 m/s every second. Therefore, one second after starting with an initial velocity of 5 m/s upward, the object will have a velocity of 5 m/s downward.
In summary, assuming the object is in free fall near the surface of the Earth, its initial velocity of 5 m/s upward will be reversed by the acceleration due to gravity, resulting in a velocity of 5 m/s downward one second later.
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Help please!!! Are forests a renewable resource? Are they ordinarily used in a renewable way? How can forests be more sustainably?
Answers
What is the mass of a 37.0 N
weight?
m
=
= [ ? ] kg
Answers
Answer: 3.775 KG
Explanation: W = 37 N
m = ?
AS WE KNOW THAT
W = mG
37 = m 9.8
m = 37/9.8
m = 3.775 KG
What minimum speed does a 100 g puck need to make it to the top of a 2.9-m-long, 34° frictionless ramp?
Answers
The minimum speed needed for the 100 g puck to reach the top of the ramp is approximately 6.0 m/s.
The minimum speed needed for a 100 g puck to reach the top of a 2.9 m long, 34° frictionless ramp, we can use the principles of conservation of energy.
The potential energy at the top of the ramp is given by the equation PE = mgh, where m is the mass (0.100 kg) of the puck, g is the acceleration due to gravity (9.8 m/s²), and h is the vertical height of the ramp.
The vertical height can be calculated using the equation h = L * sin(θ), where L is the length of the ramp (2.9 m) and θ is the angle of the ramp (34°).
Substituting the values into the equation, we have h = 2.9 m * sin(34°) ≈ 1.572 m.
Now we can calculate the minimum speed needed to reach the top of the ramp. The initial kinetic energy is given by KE = 0.5 * m * \(v^{2}\), where v is the velocity of the puck.
Since there is no friction, the total mechanical energy is conserved. Thus, the initial kinetic energy is equal to the potential energy at the top of the ramp. Therefore, we have KE = PE.
Substituting the values, we have 0.5 * 0.100 kg * \(v^2\) = 0.100 kg * 9.8 m/s² * 1.572 m.
Simplifying the equation, we find that \(v^2\) = 2 * 9.8 m/s² * 1.572 m.
Taking the square root of both sides, we find that v ≈ √(2 * 9.8 m/s² * 1.572 m).
Evaluating the expression, we find that v ≈ 6.0 m/s.
Therefore, the minimum speed needed for the 100 g puck to reach the top of the ramp is approximately 6.0 m/s.
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an object near the surface of a planet falls 54m in 3s. what is the acceleration due to gravity on that planet
Answers
Answer:
12s
Explanation: