A spring has a constant of 100 N/m. What Force does the spring exert on you if you stretch it a distance of 0.5 m?

The vectors can be expressed using unit vectors as follows:

Vector A = 96N i + 96N j + 0N k

Vector B = 76.6N i + 64.3N j + 0N k

Vector C = 64N i + 48N j + 0N k.

In the given diagram, let's consider the vectors as follows:

Vector A with magnitude 120N, Vector B with magnitude 100N, and Vector C with magnitude 80N.

To express these vectors using unit vectors i, j, and k, we need to determine their respective components in the x, y, and z directions.

For Vector A (120N), we have the following information:

Magnitude = 120N

Direction: X-axis (cosine component) with an angle of 37° and Y-axis (sine component) with an angle of 53°.

Using the trigonometric values provided:

cos37° = 0.8 and sin53° = 0.8

Therefore, the components of Vector A are:

Ax = 120N * 0.8 = 96N (in the X-direction)

Ay = 120N * 0.8 = 96N (in the Y-direction)

Az = 0N (no component in the Z-direction)

Thus, Vector A can be written as 96N i + 96N j + 0N k.

Similarly, using the trigonometric values for Vector B and Vector C, we can calculate their components:

For Vector B (100N):

Bx = 100N * cos40° = 100N * 0.766 = 76.6N

By = 100N * sin40° = 100N * 0.643 = 64.3N

Bz = 0N

Vector B can be expressed as 76.6N i + 64.3N j + 0N k.

For Vector C (80N):

Cx = 80N * cos37° = 80N * 0.8 = 64N

Cy = 80N * sin37° = 80N * 0.6 = 48N

Cz = 0N

Vector C can be written as 64N i + 48N j + 0N k.

In summary, the vectors can be expressed using unit vectors as follows:

Vector A = 96N i + 96N j + 0N k

Vector B = 76.6N i + 64.3N j + 0N k

Vector C = 64N i + 48N j + 0N k.

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Answer:

1g/cm3

Explanation:

volume of block is 3 cubed which is 27 cm3

we know density is m/v so d= 27g/27cm3

which is 1g/cm3

if my answer helps please mark as brainliest

Answer:

Uh, I could be wrong but doesn’t it mean that the wave and particle are reacting together to make light? I think it’s something like that... I hope this helps!

The net force applied to the car is 41300 Newtons.

The net force applied to an object can be determined using Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

In this case, the mass of the racing car is given as 700 kg, and the acceleration is 59 m/s². We can use the equation F = m * a, where F is the net force, m is the mass, and a is the acceleration, to calculate the net force.

Substituting the given values into the equation, we have:

F = 700 kg * 59 m/s²

F = 41300 N

Therefore, the net force applied to the car is 41300 Newtons.

The net force represents the overall force acting on the car, which is responsible for its acceleration. In this scenario, the car is experiencing a net force of 41300 N, which is causing it to undergo uniform acceleration of 59 m/s².

This force is the result of various factors, such as the engine power, aerodynamic forces, and the interaction between the tires and the road surface.

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Answer:

a and f

Explanation:

Options A and F explain the properties of a liquid. Liquid can change shape to conform to a container., It will expand to completely fill a closed container.

The liquid is a virtually incompressible fluid that adapts to its container's shape while maintaining a constant volume regardless of pressure. It is thus one of the four fundamental states of matter.

A liquid is made up of little vibrating matter particles called atoms that are bound together by intermolecular connections.

There is no defined shape (it assumes the shape of its container, but there is a certain volume. Although particles are free to travel over one another, they remain attracted to one another.

The properties of the liquid given in the options are as follows;

A.Liquid can change shape to conform to a container.

F.It will expand to completely fill a closed container.

Hence options A and F explain the properties of a liquid]

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Answer:

When an object is thrown, the thrower pushes the object. This causes the object to move in a  

Explanation:

The entire motion of an object, regardless of direction.

In physics, motion is that the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of regard to an observer and measuring the change in position of the body relative to that frame with change in time. The branch of physics describing the motion of objects without regard to their cause is called kinematics, while the branch studying forces and their effect on motion are named dynamics.

If an object isn't changing relative to a given frame of reference,  the thing is said to be at rest, motionless, immobile, stationary, or to possess a constant or time-invariant position with reference to its surroundings. Modern physics holds that, as  there's no absolute frame of reference, Newton's concept of absolute motion can't be  determined

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Answer: B

Explanation: because x is 19.4 and then the y is m/s north

Answer:

Explanation:

To convert from °C to °F , the formula is

( F-32 ) / 9 = C / 5

F is reading fahrenheit scale and C is in centigrade scale .

F = 205 , C = ?

(205 - 32) / 9 = C / 5

C = 96°C approx .

Let us calculate the heat required .

Total heat required = heat required to heat up the ice at - 20 °C  to 0°C  + heat required to melt the ice + heat required to heat up the water at  0°C to

96°C.

=  5 x 2.04 x (20-0) +  5 x 336 + 5 x ( 96-0 ) x 4.2  kJ .

= 204 + 1680 + 2016

= 3900 kJ .

Answer:

215.5 m/s

Explanation:

Given that:

the wavelength λ = 668 km

distance (d) = 3180 km

time t = 4.81 hr

\(a) speed (v) =\dfrac{distance}{time}\)

\(speed (v) =\dfrac{3180}{4.1}\)

\(speed (v) =775.61 \ km/h\)

\(speed (v) =(\dfrac{775.61\times 1000 }{3600}) \ m/s\)

\(speed(v) = 215.5 \ m/s\)

The frequency is:

\(f = \dfrac{v}{\lambda}\)

\(f = \dfrac{215.5 }{668 \times 1000}\)

\(f = 3.226 \times 10^{-4} \ Hz\)

c)

The period:

\(T = \dfrac{1}{f}\)

\(T = \dfrac{1}{3.226 \times 10^{-4}}\)

T = 3099.8 seconds

Answer:

D. Neptune, Uranus, Jupiter

Explanation:

Just took test

Answer:

Explanation:

a. The compact car going 70 MPH has more kinetic energy than the tractor trailer going 15 MPH. Kinetic energy is proportional to the square of the velocity, so even though the tractor trailer may have more mass, the higher velocity of the compact car results in greater kinetic energy.

b. The SUV and the pickup truck have the same kinetic energy since they have the same mass and velocity.

c. The compact car going 45 MPH has the most kinetic energy since it has the highest velocity out of the three vehicles. The SUV going 35 MPH has less kinetic energy, and the school bus going 15 MPH has the least kinetic energy.

The expression \(X^{N} + Y^{N}\)is not divisible by X - Y (where Y is not equal to 0).

To determine whether the expression \(X^{N} + Y^{N}\) is divisible by X - Y (where Y is not equal to 0), we can use the factor theorem and the property of binomial expansion.

The factor theorem states that if a polynomial P(x) is divisible by (x - a), then P(a) equals zero. In our case, if \(X^{N} + Y^{N}\) is divisible by (X - Y), then when we substitute X = Y into the expression, the result should be zero.

Let's substitute X = Y into the expression:

\(Y^{N} + Y^{N}\)

Since \(Y^{N}\) is equivalent to \(Y^{N}\) , the expression becomes:

2(\(Y^{N}\))

We can see that the expression 2(\(Y^{N}\)) is not equal to zero unless Y is equal to zero. Therefore, if Y is not equal to zero, \(X^{N} + Y^{N}\) is not divisible by X - Y.

In summary, unless Y is equal to zero, the expression \(X^{N} + Y^{N}\) is not divisible by X - Y according to the factor theorem and the given condition.

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The water balloon that is dropped by the student 10 meters above the ground, will hit the ground after 1.0s of falling (in 1.4 s).

To find the time we need to use the equation that related the time with the height and the acceleration due to gravity, that is to say, the first equation from the two given, but in the vertical direction:

\( y_{f} = y_{0} + v_{0}t + \frac{1}{2}at^{2} \)   (1)

Where:

\( y_{f}\): is the final height = 0

\( y_{0}\): is the initial height = 10 m

\( v_{0}\): is the initial velociy = 0 (it is dropped)          

a: is the acceleration due to gravity = -9.8 m/s² (it is negative because its direction of motion is downward)

t: is the time =?  

Solving equation (1) for t, we have:

\( 0 = 10 m - \frac{1}{2}gt^{2} \)

\( t = \sqrt{\frac{2*10 m}{9.8 m/s^{2}}} = 1.4 s \)

Therefore, the ballon will hit the ground after 1.0s of falling.

We used the first given equation but in the y-direction, because the equation x=x₀+v₀t+(1/2)at², considers a motion in the horizontal direction, and the ball is falling (y-direction). We did not use the other equation (v = v₀ + at) because we do not know the final velocity of the ball before it hits the ground (v).

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Answer:

The time it takes for the balloon to hit the ground is 1.4 seconds. So the answer is the balloon would hit the ground after 1.0 s of falling.

Explanation:

The answer can be found by using the equation  \(x=x_{0}+v_{0}t+\frac{1}{2}at^{2}\)

x is the position; the balloon falls to the ground, so \(x = 0\)

x0 is the initial position; the balloon is 10 meters high, so \(x_{0} = 10\)

t is the time; we are solving for time

a is the acceleration; in this case it is gravity (9.8 m/s^2), so  \(a = 9.8\)

*we do not need v0, or initial velocity, for this problem

the equation now looks like this  \(0=10-(\frac{1}{2}9.8)t^{2}\)

**because the acceleration is gravity and the balloon is falling downwards, the acceleration becomes negative (-9.8 m/s^2)

1) multiply 9.8 by 1/2 inside the parenthesis

\(0=10-(\frac{1}{2}9.8)t^{2}\)

\(0=10 -(4.9)t^{2}\)

\(0=-4.9t^{2} + 10\)

2) add 4.9t^2 to both sides of the equation

\(4.9t^{2} = 10\)

3) divide both sides by 4.9

\(\frac{4.9t^{2}}{4.9}= \frac{10}{4.9}\)

\(t^{2} = 2.040816\)

4) find the square root

\(\sqrt{t} = \sqrt{2.040816}\)

\(t=1.4\)

This is how we can use the equation  \(x=x_{0}+v_{0}t+\frac{1}{2}at^{2}\)  to find the answer 1.4 seconds.

the balloon hits the ground after falling for 1.4 seconds.

Answer:

1 and 5

Explanation:

potential energy is movement energy, and at 1 and 5 there is a lot of kinetic energy (built up energy) and not a lot of potential energy

Answer:

13.9 m/s.

Explanation:

Since the vertical velocity of the skydiver is constant at v = 7.0 m/s, we find the time, t it takes him to drop from a height of h = 70 m.

So, distance = velocity time

h = vt

t = h/v = 70 m/7 m/s = 10 s

This is also the time it takes him to move horizontally a distance of d = 120 m to the target.

So, his horizontal velocity is v' = distance/time = d/t = 120m/10 s = 12 m/s.

Since both vertical and horizontal velocities are perpendicular, we add them vectorially to obtain the skydivers total speed, V.

So, V = √(v² + v'²)

= √((7.0 m/s)² + (12.0 m/s)'²)

= √(49 m²/s² + 144 m²/s²)

= √(193 m²/s²)

= 13.9 m/s.

The direction of this velocity is Ф = tan⁻¹(v/v')

= tan⁻¹(7 m/s/12 m/s)

= tan⁻¹(0.5833)

= 30.3°

Answer:

Explanation:

Writing out the Newton's Law pf Cooling:

dT/dt = -k * (T - A),

where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.

If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C,

T = 100

A = 25

dT = 100 - 90 = 10

dt = 1

Putting the figures into the equation:

10/1 = -k * (100 - 25)

k = -10/75°C

After 4 minutes, dT/4 = 10/75 (100 - 25) = 10

dT = 40

Temperature after 4 minutes = 100 - 40 = 60°C

The temperature of a cup of coffee varies according to Newton's Law of Cooling, the temperature of the coffee after 4 minutes is approximately 67°C.

To tackle this problem, we can apply Newton's Law of Cooling's differential equation and solve it using variable separation.

dT/dt = -k(T - A)

At t = 0 (initial condition): T = 100°C

At t = 1 minute: T = 90°C

dT/dt = -k(T - A)

At t = 0: dT/dt = -k(100 - 25)

So,

-10 = -k(75)

k = 10/75

Separating variables and integrating, we have:

1/(T - A) dT = -k dt

∫(1/(T - A)) dT = ∫(-k) dt

ln|T - A| = -kt + C

ln|100 - 25| = 0 + C

ln|75| = C

So, the equation will be:

ln|T - A| = -kt + ln|75|

ln|(T - 25)/(75)| = -kt

Now,

ln|((T - 25)/(75))| = -(10/75)(4)

|((T - 25)/(75))| = \(e^{(-40/75)\)

T - 25 = ± 75 *  \(e^{(-40/75)\)

T = 25 ± 75 *  \(e^{(-40/75)\)

T ≈ 25 ± 42.42

Therefore, the temperature of the coffee after 4 minutes is approximately:

T ≈ 25 + 42.42 = 67.42°C

Thus, the temperature of the coffee after 4 minutes is approximately 67°C.

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Answer:

#1 - True (touch) charging when electric conductors actually touch one another.

#2. True - electrical charges are conserved (not destroyed)

Answer:

See below

Explanation:

Total distance = 300 + 100 = 400 meters in 60 + 20 = 80 seconds

   400 m / 80 s = 5 m/s

If you are using DISPLACEMENT:
 displacement =   sqrt  (  ( 300 + 100 cos 45)^2 + (100sin 45)^2 ) = 377.4 m

     in 80 seconds        377.4 / 80 = 4.7 m/s

The special and general theories of relativity and Albert Einstein's audacious theory that light is a particle are his most famous works as a physicist and Nobel winner. The most well-known scientist of the 20th century is perhaps him.

In March 1879, he was born in Ulm, Württemberg. He had a great interest in nature and the capacity to comprehend challenging mathematical ideas even as a young man in Munich. He had an unremarkable high school experience, doing exceptionally well in arithmetic but completely failing the classics, which were then thought to be crucial for anybody planning to attend college. He detested school's dreary regimentation and uncreative atmosphere.

The second study established a lot of information regarding the nature of molecules and explained Brownian motion, which is the random jostling of molecules floating in a fluid. 16 years later, this study helped him win the physics Nobel Prize.

However, his third work, "On the Electrodynamics of Moving Bodies," was left out of the award's wording. The third article was the one that would have the biggest impact on contemporary physics. It included Einstein's Special Theory of Relativity, which greatly simplified how we think about how radiation, like light, interacts with matter. Speaking about one body moving and another being motionless has no real significance, according to Einstein. Only in connection to one other can bodies be conceived of as moving;

This specifically implies that, regardless of the frame of reference, electromagnetic radiation's (such as light's) speed remains constant. Even well-known scientists struggled to comprehend this theory because of Einstein's insightful and audacious viewpoint. But over time, when the predictions made by his theory were repeatedly verified, the Special Theory of Relativity finally transformed how scientists thought about matter, space, time, and everything that interacts with them.

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correlation  between the length of the semimajor axis and the orbital period is given by Kepler's 3rd law P² = kA³

Kepler's 3rd law is given as

P² = kA³

where

P = period, days

A = semimajor axis, AU

k = constant

Given: for mars

P = 687 days

A = 1.52 AU

Therefore

k = P²/A³

= 687²/1.52³

= 1.3439 x 10⁵ days²/AU³

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Answer:   There is a positive correlation. A longer semimajor axis corresponds to a longer orbital period.

Explanation:

Answer:

Circuit B

Explanation:

To know the correct answer to the question, we shall determine the reading of the ammeter i.e the current in each circuit. This can be obtained as follow:

For circuit A:

Resistance (R) = 5 ohms

Voltage (V) = 1.5 V

Current (I) =?

V = IR

1.5 = I × 5

Divide both side by 5

I = 1.5 / 5

I = 0.3 A

For circuit B:

We'll begin by calculating the total resistance in the circuit. This can be obtained as follow:

Resistance 1 (R₁) = 5 ohms

Resistance 2 (R₂) = 5 ohms

Total resistance (Rₜ) =?

Since they are in parallel connections, the total resistance can be obtained as illustrated below:

Rₜ = R₁ × R₂ / R₁ + R₂

Rₜ = 5 × 5 / 5 + 5

Rₜ = 25 / 10

Rₜ = 2.5 ohms

Finally, we shall determine the current in the circuit.

Resistance (R) = 2.5 ohms

Voltage (V) = 1.5 V

Current =?

V = IR

1.5 = I × 2.5

Divide both side by 2.5

I = 1.5 / 2.5

I = 0.6 A

For circuit C:

We'll begin by calculating the total resistance in the circuit. This can be obtained as follow:

Resistance 1 (R₁) = 5 ohms

Resistance 2 (R₂) = 5 ohms

Total resistance (Rₜ) =?

Since they are in series connections, the total resistance can be obtained as illustrated below:

Rₜ = R₁ + R₂

Rₜ = 5 + 5

Rₜ = 10 ohms

Finally, we shall determine the current in the circuit.

Resistance (R) = 10 ohms

Voltage (V) = 1.5 V

Current =?

V = IR

1.5 = I × 10

Divide both side by 10

I = 1.5 / 10

I = 0.15 A

SUMMARY:

Circuit >>>>>>> Current

A >>>>>>>>>>>> 0.3 A

B >>>>>>>>>>>> 0.6 A

C >>>>>>>>>>>> 0.15 A

from the above calculations, circuit B has the highest ammeter reading.

The number of revolutions the tire makes in 6 s is

N = (58π)/(12π) = 4.83 rev.

What is revolutions?

Revolutions min physics is the study of the physical aspects of revolutions, including the forces and motions that cause them, the structures and systems that are produced in their wake, and the physical processes that lead to their initiation and termination. It has roots in the study of revolutions in the social sciences, but has developed its own principles and techniques to study physical phenomena related to revolutions. These techniques include the use of mathematical models, experiments, numerical simulations, and computer visualizations.

The linear velocity of a point on the tire's circumference is given by

v = (dπ)/t

where d is the diameter of the tire and t is the time.

Substituting d = 58 cm and t = 6 s, the linear velocity of a point on the tire's circumference is

v = (58π)/6 m/s.

The number of revolutions the tire makes in 6 s is given by

N = (v/2π)

Substituting v = (58π)/6 m/s, the number of revolutions the tire makes in 6 s is

N = (58π)/(12π) = 4.83 rev.

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Answer:

Car X

Explanation:

The distance traveled by each car is equal to the area under the line of the velocity vs time graph. Since the area under the line for Car X is greater than the area under the line for Car Y, we get that the car that has traveled farther is Car X.

Therefore, the answer is Car X.

Workdone:-

\(\\ \tt\longrightarrow Force\times Displacement \)

\(\\ \tt\longrightarrow 500(100)\)

\(\\ \tt\longrightarrow 50000J\)