Solving Dynamics Problem: Normal Force at Bottom of Hill?

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To determine the normal force on a 2kg sled at the bottom of a hill with a speed of 4m/s and a radius of curvature of 1.5 meters, knowledge of friction is not necessary. The key is to analyze the forces acting on the sled using a free body diagram. The normal force can be calculated by summing the forces in the normal direction, leading to the equation N = m*g + m*(v^2/r). This approach confirms that the problem can be solved without considering friction, simplifying the calculation. The discussion concludes that the method is straightforward and effective.
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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!
 
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judonight said:

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
 
nrqed said:
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 :blushing: ...
 
Yes, it's that simple.
 
Doc Al said:
Yes, it's that simple.


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