# Dynamics problem

## Homework Statement

A 2kg sled slides down a curved path where it's velocity at the point directly at the bottom of the hill it has speed 4m/s. If the radius of curvature at the point at the bottom of the hill is 1.5 meters, determine the normal force exerted on the sled at that point.

Is the knowledge of friction properties neccessary?

## The Attempt at a Solution

Initially I am unsure if the knowledge of friction is absolutely neccesary to solve this problem.

I think that the first step is to break the sled up at the bottom of the hill into normal and tangential coordinates. The normal acceleration is v^2/r, I'm not sure if this is the first step or not.

Guess I need a clue how to start this problem, and whether or not knowledge of friction is absolutely neccessary.

TIA!

nrqed
Homework Helper
Gold Member

## Homework Statement

A 2kg sled slides down a curved path where it's velocity at the point directly at the bottom of the hill it has speed 4m/s. If the radius of curvature at the point at the bottom of the hill is 1.5 meters, determine the normal force exerted on the sled at that point.

Is the knowledge of friction properties neccessary?

## The Attempt at a Solution

Initially I am unsure if the knowledge of friction is absolutely neccesary to solve this problem.

I think that the first step is to break the sled up at the bottom of the hill into normal and tangential coordinates. The normal acceleration is v^2/r, I'm not sure if this is the first step or not.

Guess I need a clue how to start this problem, and whether or not knowledge of friction is absolutely neccessary.

TIA!

No, you don't need to know anything about the friction force because you only work exactly at the bottom of the hill. To see what I mean, draw a free body diagram. Now, look at the forces along the direction normal to the surface and use the fact that the acceleration normal to the surface is v^2/r as you said. You will be able to find the normal force without having to worry about friction (your answer will be valid whether there is friction or not).

Patrick

No, you don't need to know anything about the friction force because you only work exactly at the bottom of the hill. To see what I mean, draw a free body diagram. Now, look at the forces along the direction normal to the surface and use the fact that the acceleration normal to the surface is v^2/r as you said. You will be able to find the normal force without having to worry about friction (your answer will be valid whether there is friction or not).

Patrick

Ok thanks! I was worried I didn't word the question well enough...

So, in the normal direction I simply sum the forces = m*a = N - W ? [N being the normal, W being weight, a being v^2/r] and just solve for N?!

N = m*g + m* (v^2/r) ?

If it is that simple, I'm imbarassed ...

Doc Al
Mentor
Yes, it's that simple.

Yes, it's that simple.

Ok, thanks for letting me waste your time! Geez...