Since the height of the books is constant, there is no change in potential energy. Similarly, since the speed of the books is constant, there is no change in kinetic energy. By the work-energy theorem, work is equal to the change in mechanical energy (including potential and kinetic). If there is zero change in energy, the work done must also be zero.

We can also look at this problem in terms of forces. There is zero acceleration on the books, since they do not move in the vertical direction and the horizontal velocity is constant. If there is no acceleration, then there is no force. If there is no force, then there is no work, according to Newton's second law.

The amount of work performed to get child 1 down the ramp is equal to the amount of kinetic energy gained by her from top to bottom, via the work-energy theorem. Unfortunately, we are not given her kinetic energy. We can't use the 5m/s in the passage, because she stops herself before sliding to the lake surface.

We must instead recognize the potential energy lost is equal to kinetic energy gained. The potential energy that she has lost is given by mgh.

This is an application of the work-energy theorem. The amount of work done by the force of gravity to move child 1 down the ramp is equal to force * distance, as well as equal to the amount of kinetic energy picked up down the ramp.

The force down the ramp is equal to mg*sin(30^o) = 600J * 0.5 = 300J

This question can be answered using conservation of energy. Having an understanding of the work-energy theorem allows us the knowledge that changing kinetic energy is a form of work, and that work can be a form of energy. In this particular question, the only force acting on the block to slow it down is the force of friction from the rough surface. As we know, work is equal to force times distance.

Because the block started with a certain amount of kinetic energy, and then is brought to a complete stop, all of that kinetic energy is transferred to work done by the force of friction over a distance of six meters.

Because the block had a velocity of  on a smooth surface and ends with a velocity of  at rest, we can calculate the change in kinetic energy.

The kinetic energy is completely converted to the work done by friction.

We can then use the first equation for work to determine the force of friction.

Because the force of friction is parallel to the displacement of the box, we can solve for the work done by friction using the following equation.

Now, we need to define the force of friction or .

In this formula,  equals acceleration. In this case, acceleration equals acceleration due to gravity in the x-direction; therefore, use the cosine function.

Insert the value of acceleration due to gravity for .

Now, we can solve for the work done by friction.

The Doppler shift equation for light is , where f is the source frequency, f' is the observed frequency, v is the relative velocity between source and observer, and c is the speed of light.

When the source and observer are moving closer together, v is positive, so the observed frequency is greater than the source frequency. Greater frequency also implies shorter wavelength, so visible light is shifted towards the blue end of the spectrum.

In this scenario the Doppler effect is described by the following equation. 

Using the values from the problem, we know that v_o is zero and v_f is 15m/s. v is 340m/s and f_s is 790Hz.

The equation for Doppler effect is   , where the + sign applies when the source and observer are moving farther apart, and the - sign applies when they are moving closer together. In these equations, v is the speed of sound, 340m/s,  is the frequency of sound emitted by the source,  is the freqency perceived by the observer, and  is the relative velocity between the source and observer.

We can apply this equation to the first part of the motion, as the truck moves closer to the observer, to solve for the velocity of the truck.

Now we can plug this velocity into the equation again for when the truck moves farther away from the observer and solve for .

This question is asking us how the frequency changes when one object moves directly towards another; thus, this is a Doppler effect problem. Remembering back to our Doppler effect formula, we know that, where f is the frequency heard by the recipient (the person at the concert), v_r is the velocity of the receiver, v_s is the velocity of the source, and f₀ is the original frequency.

In our case, the speaker is not moving, so v_s is zero. v_r is positive when the person is walking towards the speaker, so the frequency heard will be higher than the original frequency.

This question is asking us how the frequency changes when one object moves directly away from another; thus, this is a Doppler effect problem. Remembering back to our Doppler effect formula, we know that, where f is the frequency heard by the recipient (the person at the concert), v_r is the velocity of the receiver, v_s is the velocity of the source, and f₀ is the original frequency. 

In our case, the speaker is not moving, so v_s is zero. v_r is negative when the person is walking towards the speaker, so the frequency heard will be lower than the original frequency. We can calculate the heard frequency using our equation.