# 3 Questions in regards to WORK AND ENERGY

• mmiller39
In summary: So to answer the question, the engine would need to do 43.0 W every second in order to launch the projectile at a speed of 2 v.
mmiller39
I am attempting 3 questions I have worked them out but to no avail. I wonder if I am on the right track:

1st Question:

Starting from rest at the top, a child slides down the water slide at a swimming pool and enters the water at a final speed of 5.00 m/s. At what final speed would the child enter the water if the water slide were twice as high? Ignore friction and resistance from the air and the water lubricating the slide.

Here I am using the principal of conservation of mechanical energy that can be rewritten as follows:

Vf = Sqrt(Vo^2 + 2g(ho - hf)

So I assign a random number (I used 5) to hf and I get:

5.0 m/s = Sqrt(0 + 19.6(Ho - 5))

5 = Sqrt(19.6ho - 98)

25 = 19.6ho - 98

ho = 6.2755

So since the H is twice what it would be I used 12.551

And get:

Vf = Sqrt(Vo^2 + 19.6(12.551 - 5))

Vf = 12.16 <------Wrong...is there somewhere I went wrong?

SECOND QUESTION:

A 915-kg car starts from rest at the bottom of a drive way and has a speed of 3.00 m/s at a point where the drive way has risen a vertical height of 0.600 m. Friction and the drive force produced by the engine are the only two nonconservative forces present. Friction does -2870 J of work. How much work does the engine do?

So I used the Work Energy theorum:

Wnc = 1/2m(Vf^2 - Vo^2) - mg(ho - hf)

Wnc = 457.5(3)^2 - 8967(-6)

Wnc = 57919.5

Do you see anything wrong with my math?

THIRD QUESTION:

The power needed to accelerate a projectile from rest to its launch speed v in a time t is 43.0 W. How much power is needed to accelerate the same projectile from rest to a launch speed of 2 v in a time of t?

I am confused by the relationship here...are there any formulas that would apply here?

Thanks SO much!

Matt

For 1. Rearrange Vf to get an expression for ho, you know hf = 0. Then just stick 2*ho back into your original expression to find Vf.

Max Eilerson said:
For 1. Rearrange Vf to get an expression for ho, you know hf = 0. Then just stick 2*ho back into your original expression to find Vf.

Do I use the same equation that I used in the beginning?

Last edited:
Does anyone have any ideas for the 2nd and 3rd one?

Thanks!

For question two, do not forget that the engine is doing work not only against gravity, but also against friction.

For question three, remember that power is the rate at which work is done.

## 1. What is the definition of work in physics?

In physics, work is defined as the force applied to an object multiplied by the distance the object moves in the direction of the force. It is a measure of the energy transferred to or from an object by means of a force acting on the object.

## 2. How is work related to energy?

Work and energy are closely related concepts in physics. Work is the transfer of energy from one object to another, or from one form to another. Energy is the ability of a system to do work. So, when work is done on an object, energy is transferred to that object, and when work is done by an object, energy is transferred away from that object.

## 3. What is the difference between kinetic and potential energy?

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object possesses due to its position or state. Kinetic energy is directly related to the mass and speed of an object, while potential energy is related to the height, position, or configuration of an object in a gravitational or other force field.

## 4. How is the work-energy theorem applied in real-world situations?

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. This theorem is applied in various real-world situations, such as calculating the work done by a car's engine to accelerate a car, or the work done by a person in lifting a heavy object. It is also used in analyzing the motion of objects in roller coasters and other amusement park rides.

## 5. Can work and energy be negative values?

Yes, both work and energy can have negative values. Negative work occurs when the force applied to an object is in the opposite direction of the object's motion, resulting in a decrease in the object's kinetic energy. Negative energy values can also occur, such as in the case of potential energy, where a decrease in height or position can result in a decrease in potential energy.

Replies
2
Views
505
Replies
1
Views
4K
Replies
12
Views
2K
Replies
23
Views
1K
Replies
8
Views
1K
Replies
9
Views
1K
Replies
5
Views
904
Replies
6
Views
1K
Replies
3
Views
1K
Replies
5
Views
8K