Solve 2 Block Swing Homework: Find Mass m

[postfan]

Homework Statement

A box of mass M is at rest on a horizontal table. The coefficient of static friction between the box and the table is k. The box is connected by a taut string to a block of unknown mass m , initially held horizontally as shown and then released. The box begins to slide at the instant the block reaches the bottom point of its swing. Find the mass m of the block.

Homework Equations

The Attempt at a Solution

I took the force of gravity, mg, and set it equal to the friction force between the box and the table, kMg, getting m=k*M.

 

[gneill]

Gravity and friction are not the only forces involved. The block m is following a circular path...

 

[postfan]

Is the third force angular acceleration?

 

[gneill]

Is the third force angular acceleration?

Acceleration is not a force. What force is invoked to cause a body to move in a circular path?

 

[postfan]

Is it a centripetal force?

 

[greendog77]

Yes, the mass must experience a centripetal force in order to move in a circular path. So how is this force provided?

 

[postfan]

The force is provided by the circular swinging of the rope and is equal to mv^2/r. Is that right?

 

[gneill]

The force is provided by the circular swinging of the rope and is equal to mv^2/r. Is that right?

The rope is the means by which the centripetal force is applied to the moving mass, yes. In addition, the rope also must supply a force that counteracts the weight of the mass at the bottom of the swing. Both forces are then acting in the same direction. What's the total?

 

[postfan]

The total is mg+mv^2/r. Is that correct?

 

[gneill]

The total is mg+mv^2/r. Is that correct?

Yes. You have enough information to continue. So rather than inching along one confirmation at a time, how about you take a stab at the full solution now?

 

[postfan]

Ok, I got m=2gkMr/(2^5/6*v^2+2*g*r). Is that right?

 

[gneill]

Ok, I got m=2gkMr/(2^5/6*v^2+2*g*r). Is that right?

Show your work. You've introduced new variables...

What is v? You should be able to determine v from the given information (I assume that r is given, although you didn't say so, right?)

 

[postfan]

r is not given in the problem and I can't figure out what v is.

 

[gneill]

r is not given in the problem and I can't figure out what v is.

If r is not given, then you have no choice but to introduce it as a variable. No problem. But you should be able to determine v, after all, it's just a mass falling though some distance in a gravitational field. Think about conservation rules.

 

[postfan]

Is v equal to pi*r*g/2, giving a final answer of m=k*M/(g*r)?

 

[gneill]

Is v equal to pi*r*g/2?

No. There's no pi involved; you want the change in height (in the gravitational field) in order to find the change in potential energy. What energy is it "traded" with, and what expression defines it?

 

[postfan]

Ok so is v=sqrt(2*g*r)?

 

[gneill]

Ok so is v=sqrt(2*g*r)?

Yup. Carry on.

 

[postfan]

Ok so the final answer is 1/3*k*M. Is that right?

 

[gneill]

Ok so the final answer is 1/3*k*M. Is that right?

Looks good!

 

[postfan]

Thanks a ton for your help!

 

[gneill]

You're welcome.