Heres a tough one i had on my final im dying to find out how to do it

[xxacefirexx]

I don't remember the question verbatim, but here is all the info

Homework Statement

There is a mass attached to a rope which is attached to a pole. It is set to rotate on a horizontal surface (basic circular motion scenario). There is no kinetic friction along the table, but there is air friction.

The magnitude of air friction is related to velocity with the equation .2v.
m=3 kg
r=2 m
v(initial)=10 m/s

What is the centripetal acceleration after 5 s.

Homework Equations

F=ma=m(v^2/r)

The Attempt at a Solution

i know you got to integrate the air friction function over the 5 s interval, but i can't express it in terms of t.

I am completely lost, please help. I know I got it wrong, but i really want to know how to do it.

Thanks!

 

[PhanthomJay]

I don't remember the question verbatim, but here is all the info

Homework Statement

There is a mass attached to a rope which is attached to a pole. It is set to rotate on a horizontal surface (basic circular motion scenario). There is no kinetic friction along the table, but there is air friction.

The magnitude of air friction is related to velocity with the equation .2v.
m=3 kg
r=2 m
v(initial)=10 m/s

What is the centripetal acceleration after 5 s.

Homework Equations

F=ma=m(v^2/r)

The Attempt at a Solution

i know you got to integrate the air friction function over the 5 s interval, but i can't express it in terms of t.

I am completely lost, please help. I know I got it wrong, but i really want to know how to do it.

Thanks!

F=mv^2/r is the correct centripetal force formula for the tension in the rope, but the problem is asking for the centripetal acceleration only. You need first, however, to use Newton's 2nd law in the tangential direction, where the tangential acceleration is not constant. Thus,
use F=m(dv/dt), where F is the given air resistance force (presumably in force units of Newtons). You get a first order differential equation you must solve of the form -kv = mdv/dt. Solve for v and don't forget the boundary condition. Is this where you are stuck?

 

[m2003]

I understand your frustration and eagerness to find the solution to this problem. Let's break it down step by step.

First, we need to understand the forces acting on the mass. In this case, we have the tension force from the rope and the air friction force. The tension force is providing the centripetal force necessary for circular motion, while the air friction force is acting in the opposite direction, slowing down the mass.

Next, we can use the formula F=ma to find the net force acting on the mass. In this case, the net force is equal to the tension force minus the air friction force. We can write this as:

m*a = T - 0.2*v

where T is the tension force and v is the velocity.

Now, we need to take into account the fact that the velocity is changing over time. This means we need to integrate the air friction function (0.2v) over the 5 second interval. This will give us the total air friction force acting on the mass during that time period.

Once we have the total air friction force, we can plug it back into our equation and solve for the acceleration. This will give us the centripetal acceleration after 5 seconds.

I hope this helps guide you towards finding the solution to this problem. Remember to always break down the problem into smaller parts and use the appropriate equations to solve for the unknowns. Good luck!