Solving Strange Friction AP Problems with m, R, mu, v

In summary: A small block of mass m is on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is mu; therefore, the speed v of the block decreases. In terms of m, R, mu, and v, find expressions for:a. the frictional force on the block.I got this part, friction is the centripetal force or mv^2/R.b. the block's tangential acceleration, dv/dt.c. the time required to reduce the speed of the block from an initial value v0 to v0/3.I haven't formally taken
  • #1
turdferguson
312
0
A small block of mass m is on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is mu; therefore, the speed v of the block decreases. In terms of m, R, mu, and v, find expressions for:

a. the frictional force on the block. I got this part, friction is the centripetal force or mv^2/R.

b. the block's tangential acceleration, dv/dt.

c. the time required to reduce the speed of the block from an initial value v0 to v0/3.

I haven't formally taken calc yet (this is an APC mechanics free response), but I think I have a good enough understanding of it. The thing that hangs me up is that friction is not proportional to weight as usual. The only friction is caused by the hoop. The force on the hoop at an instant is the velocity. Does this mean friction = mu x v?.
I think I'm on the right track, the sliding causes a friction force which lowers the velocity which in turn lowers the friction force, lowering the velocity, etc. But how do I express this mathematically and answer the last two parts?
 
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  • #2
The friction will still be proportional to the normal force.
 
  • #3
Thanks a lot, its not as hard as I thought then. So the opposite of friction (mu x mg) is ma and a=-mu x g??
 
  • #4
The normal force of a mass on a horizontal surface is often equal to mg, not always, though. I think that must be where you are getting your mu x mg from. But it doesn't apply in this case, because only fhe hoop has friction, so the weight of the mass (mg) doesn't enter into this problem at all. I don't see g as being relevant to solving this problem, since the hoop is horizontal.

Instead, focus on the force perpendicular to the wall of the hoop. That's the normal force, N. Then the frictional force will be mu*N as always, and that is what is creating the tangential acceleration. I think you are very close to solving it.

Dorothy
 

Related to Solving Strange Friction AP Problems with m, R, mu, v

1. What is the equation for solving strange friction AP problems with m, R, mu, and v?

The equation for solving strange friction AP problems is F = m * g * R * mu * v, where F is the force of friction, m is the mass of the object, g is the acceleration due to gravity, R is the coefficient of restitution, mu is the coefficient of friction, and v is the velocity of the object.

2. How do I determine the value of mu in a strange friction AP problem?

The value of mu can be determined by using the formula mu = F / (m * g * R * v). This formula takes into account the force of friction, mass, acceleration due to gravity, coefficient of restitution, and velocity of the object.

3. Can I use this equation for any type of friction problem, or only strange friction AP problems?

This equation is specifically designed for solving strange friction AP problems, where there is a combination of normal and tangential forces acting on the object. It may not be applicable for other types of friction problems.

4. Is there a specific unit for the coefficient of friction in this equation?

The coefficient of friction is a unitless quantity, so there is no specific unit for it in this equation. However, it is important to ensure that all other variables are in consistent units (e.g. mass in kilograms, velocity in meters per second).

5. Are there any simplifications or assumptions made in this equation?

The equation assumes that the surface is flat and the object is moving in a straight line. It also assumes that the coefficient of restitution and coefficient of friction remain constant throughout the movement of the object. In reality, these values may change depending on the surface and other factors.

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