Is the Force on a Block on an Incline Dependent on Velocity?

In summary, The conversation discusses a physics homework problem involving a block sliding down a frictionless incline and then going up a semi-circle. The question is about the force on the block at a specific point. The person initially questions if the force is dependent on velocity, but then has a breakthrough and realizes it can be found using centripetal acceleration.
  • #1
smallbrain
2
0
hi, I'm stuck on my very first physics homework problem for my junior level mechanics course... i am not sure if the force in this problem is dependent on velocity.

a block of mass m slides down a frictionless incline. it is released at height h above the bottom of the loop. when it reaches the bottom, it begins going up a semi-circle of angle 45 degrees and radius R. the point where it begins going up the semi circle is labeled point A. basically, the block has acquired a certain velocity, and then starts going up a ramp. the point where the ramp begins is point A.

the question is, what is the force by the inclined track on the block at point A?

i realize the force by the track on the block is the normal force, however it appears this force would also be a function of the velocity, and not just of the mass of the block, but i am not sure. i am stuck because i am not sure if the force would simply be the normal force, or if it would be a function of the velocity (i know how to find the velocity).

am i totally wrong, and the force is simply the normal force, and not a function of the velocity? if there is acceleration upward at point A, which is what i suspect, then is it dependent on velocity (as i can only imagine it is)?

any help would be greatly appreciated.

this is problem 2-25 in thornton/marion's classical dynamics, part (a)
 
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  • #2
heh, i swear I've thought about this problem for a couple of hours total (i looked at it first yesterday), and i just had a breakthrough immediately after i posted the question.

clearly the ramp part of the system can represented as an angular system which has a certain angular velocity at point A. this will allow me to find the acceleration at that point, and thus the force! correct?
 
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  • #3
I don't think you have to go so far as to change to an angular representation of the objects position, if that's what you're saying. You know the block is undergoing centripetal acceleration, so you can use mv^2/r to find the net force on it. This is equal to the normal force plus gravity, so subtract gravity and you have your answer.
 
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1. What is force?

Force is a physical quantity that can cause a change in the motion or shape of an object. It is measured in Newtons (N) and is represented by the symbol F.

2. How is force related to velocity?

Force is directly proportional to velocity. This means that as the velocity of an object increases, the force required to maintain that velocity also increases. This is explained by Newton's second law of motion, which states that force equals mass times acceleration (F=ma). Since velocity is a type of acceleration, an increase in velocity requires a corresponding increase in force to maintain it.

3. What is the difference between force and velocity?

Force and velocity are two different physical quantities. Force is a measure of the strength or magnitude of a push or pull on an object, while velocity is a measure of an object's speed and direction of motion. Force is a vector quantity, meaning it has both magnitude and direction, while velocity is a vector quantity that only has magnitude.

4. How does force affect an object's velocity?

Force can change an object's velocity by either increasing or decreasing it. If a force is applied in the same direction as an object's velocity, it will increase the object's speed. If a force is applied in the opposite direction of an object's velocity, it will decrease the object's speed. Additionally, if the force is applied at an angle to the object's velocity, it will cause the object to change direction.

5. What is the formula for calculating force as a function of velocity?

The formula for force as a function of velocity is F=m(v/t), where F is force, m is mass, v is velocity, and t is time. This formula is derived from Newton's second law of motion (F=ma) and the equation for velocity (v=dx/dt). It can be used to calculate the force required to maintain a certain velocity or the change in force needed to achieve a desired change in velocity.

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