# Two physics KE/PE questions(and possibly more, studying for a test)

• axforts
In summary, the carpenter exerts a force of 75N on a nail, driving it 2cm into the wood board. The nail gains 1.5J of work and 1.73J of heat energy. For the second problem, there is a disagreement of results when calculating the work done by accelerating a 1200kg car up an 18m high, frictionless hill. One method yields 259.2kJ while the other yields 298080J.
axforts

## Homework Statement

a carpenter moves his .5 kg hammer at 3m/s when it contacts a nail. The nail receives an average force of 75N as it is driven 2cm int the wood board. The carpenter notices that the nail feels warm after he hits it with the hammer. How much heat energy was transferred to the nail.

W = fd

## The Attempt at a Solution

work w =force Fx distsnce D
w=75nx.02m
w=1.5j

Maybe I am supposed to do Ke = .5mv^2 and get 2.25J, then 2.25- 1.5J = .75J?

Except that was wrong?
Next problem

How much work is done by accelerating a 1200kg card from rest to a speed of 12m/s while it is movin up a frictionless hill that is 18m high.

force = mass x acceleration F= 1200x12=14400n
w=force x distance w=14400x18=259200j
=259.2kj

Except my friend is getting 298080J. Not sure whos right here. Thanks everyone!

Hes doing
W = mg(18) + .5m(12)^2

Last edited:
When you calculate the work, you do need to take into account any change in potential energy. Try that for the first problem and see if it gets you a better result.

So for the first one, I tried

5mv^2 + mgh = W + Q
W = fd = 75N * .02m
= 1.5J
.5(.5kg)(3m/s)^2 = 2.25J
= KE
.5kg * 9.8m/s^2 * .02m = PE = .98J
2.25+ .98 = 1.5 + Q

So is Q 1.73J?

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

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or state. Kinetic energy is directly proportional to the mass and velocity of an object, while potential energy is directly proportional to the mass and height of an object.

## 2. How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

## 3. Can an object have both kinetic and potential energy at the same time?

Yes, an object can have both kinetic and potential energy at the same time. For example, a ball thrown into the air has both kinetic energy due to its motion and potential energy due to its height above the ground.

## 4. How does the conservation of energy apply to these two types of energy?

The conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. In the case of kinetic and potential energy, they can be converted into each other, but the total amount of energy remains constant.

## 5. Can potential energy be negative?

Yes, potential energy can be negative. This often occurs when the reference point for measuring potential energy is chosen to be below the object's starting point, such as in the case of a roller coaster going down a hill. In this case, the potential energy at the starting point would be zero, and as the coaster moves down the hill, the potential energy becomes negative.