Motion, Work, Energy, and Power

[sp00ky]

Okay well my teacher gave me this sheet where you can prepare for the test that will be the next day. The thing is that the sheet consists of questions but no numbers or anythin' so you just have to figure it out how do approach the problems. I have most of them figured out but there might be a few that might have more than one way to do it and just making sure if there is or not.

1. Caculate the average force supplied by the brakes to stop the roller coaster given its initial velocity and stopping distance. What I think I have to do here to get the answers if there were number are:
V1 =
delta D =
V2 =
This is to find the acceleration, then
Fnet = Fbrakes
= ma

2. In the absence of friction, calculate the maximum velocity of the roller coaster given the height of the first hill.
V1 = 0
h2 = 0
Etotal1 = Etotal2
Eg1 + Ek1 = Eg2 + Ek2
Eg1 + Ek1 = Ek2
gh1 + 1/2 v1^2 = 1/2 v2^2

3. In the absence of friction, calculate the velocity oat any other point along the track given the height of the track.
Etotal1 = Etotal2
gh1 + 1/2v1^2 = 1/2 v2^2

5. Given the actualy maximum velocity of the roller coaster, calculate the energy lost to heay and noise during its descent on the first hill.
Eg - Ek = Ebust
(mgh)-(1/2mv^2) = E2

6. Given the force applied by the chain and pulley system to drag the roller coaster up to the first hill, calculate its efficiency.
%eff = deltaE/W * 100
deltaE = ma (delta D)
w = F * delta D

 

[HallsofIvy]

1. Yes, you need to find the acceleration first. Do you know a formula that relates acceleration to distance?

2. Yes, the initial potential energy will be converted to kinetic energy. Presumably the car is pulled to the top of the first hill and then released so its initial speed is 0.

3. Actually, I would say gh1= gh2+ 1/2 v2^2. h1 is the height of that "first hill" h2 is the height of the given point, v2 the speed there.

5. Yes, the difference between the initial potential energy and the kinetic energy at maximum velocity is the energy lost (Ebust?).

6. Yes, W= F* delta D (delta D is the distance the car is hauled up the first hill) is the work done. delta E is the potential energy given to the car (which would be mgh) so the efficiency, as a percent, is (delta E/W)*100.

 

[wais]

Motion, work, energy, and power are all important concepts in physics that help us understand the behavior of objects in our physical world. In this scenario, we are specifically looking at a roller coaster and how these concepts apply to its movement.

Motion refers to the movement of an object, and in this case, the roller coaster is moving along a track. Work is the transfer of energy that occurs when a force is applied to an object and it moves in the direction of the force. In the first question, we are calculating the average force applied by the brakes to stop the roller coaster. This involves using the equation F=ma, where m is the mass of the roller coaster and a is the acceleration. We can find the acceleration by using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, and s is the stopping distance. By rearranging this equation, we can find the acceleration and then use it to calculate the force applied by the brakes.

Energy is the ability of an object to do work, and it comes in different forms such as kinetic energy (energy of motion) and potential energy (stored energy). In the second and third questions, we are looking at the energy of the roller coaster at different points along the track. In the absence of friction, the total energy of the roller coaster remains constant, as shown in the equations provided. This is known as the conservation of energy.

Power is the rate at which work is done or energy is transferred. In the fifth question, we are calculating the energy lost due to heat and noise during the roller coaster's descent. This is important as it tells us about the efficiency of the roller coaster. Efficiency is a measure of how much energy is converted into useful work. In the sixth question, we use the efficiency equation to calculate the efficiency of the chain and pulley system used to drag the roller coaster up to the first hill.

In summary, understanding the concepts of motion, work, energy, and power can help us analyze and predict the behavior of objects in motion, such as the roller coaster in this scenario. By applying these concepts, we can calculate important factors like force, velocity, and energy, which are essential in designing and operating roller coasters.