# Kinetic energy and normal force

• Rowie25
In summary, the problem involves a sled with a mass of 100 kg sliding down a frictionless road with a 20 degree incline and then going up a 30 degree incline with a friction coefficient of 0.1. The questions ask for the sled's kinetic energy at the bottom of the hill, net acceleration, time to slide to the bottom, and normal force exerted on the sled. The solution involves finding the speed using the conservation of energy equation and determining the normal force using the formula mgcos(angle). Net acceleration is the sum of all forces divided by the mass. Finally, the distance the sled travels up the 30 degree incline before stopping is also asked.
Rowie25

## Homework Statement

You and your sled have a mass of 100 kg and starting from rest, slide down a very icy and frictionless road which is 20 degrees steep and 200 m long.
a. What is your kinetic energy at the bottom of the hill?
b. What is your net acceleration?
c. How long does it take you to slide to the bottom?
d. What is the normal force exerted on you and your sled?
At the bottom of the hill you change direction but not your speed and go up a hill which is 30 degrees steep and with friction coefficient .1.
e. What distance along the hill do you go before stopping?

I am not sure how to start this one. I think you have to find the speed first since KE=(1/2)mv^2. I think normal force is mgcos(angle)yhat but I don't know how to find yhat. Also is net acceleration the sum of all forces divided by the mass? I'm stuck!

Rowie25 said:
I am not sure how to start this one. I think you have to find the speed first since KE=(1/2)mv^2.
Speed is not needed, this is a conservation-of-energy question. You can check your textbook for the relevant equation if you do not know it.
I think normal force is mgcos(angle)yhat but I don't know how to find yhat.
It's universally agreed that the normal force's direction is perpendicular to the sloping surface (by definition), so it should suffice to give it's magnitude.
Also is net acceleration the sum of all forces divided by the mass? I'm stuck!
Yes, that is what they are asking for. Personally I dislike the term "net acceleration", an object only has one acceleration even if there are several forces acting on it. Just my opinion.

Ohh okay thank you! I'll work on it!

## 1. What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity.

## 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. What is normal force?

Normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface. It is also known as the support force.

## 4. How is normal force related to kinetic energy?

The normal force plays a role in determining the amount of kinetic energy an object has. If the normal force is greater, it can increase the object's kinetic energy by doing work on it. Similarly, if the normal force decreases, it can decrease the object's kinetic energy.

## 5. Can an object have kinetic energy without a normal force?

No, an object cannot have kinetic energy without a normal force. The normal force is necessary for an object to have a surface to push against and gain kinetic energy through work done by that force.

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