Question

A 0.78-kg block and a 0.56-kg block sits on a rotating disk. They are connecting by a 12-cm long string. The coefficients of static and kinetic friction between the block and disk are µs = 0.87 and µk = 0.63, respectively. The cart is on wheels and moves frictionless. The distances of the block and the cart from the center of disk are 0.23 m and 0.35 m, respectively. The block and cart are sitting (i.e., are not moving) relative to the disk. a) The disk rotates at 33 rpm. Find the acceleration of the block and the cart. b) Draw the appropriate free-body diagrams! 4 c) Write down Newton’s second law for the block and the cart! d) Find magnitudes of all forces acting both on the block and the cart! Are these forces consistent with the fact that the block and cart are sitting (i.e., are not moving) relative to the disk?

Answer 1

SOLUTION

Part (a)

For block, the centripetal acceleration is defined as:

Inserting data given values:

solving we obtain:

While that, for cart we have:

Solving we obtain:

Part (b)

For block we have:

For cart we have:

Part (c)

For block, the Newton's second Law is:

similarly, for cart we have:

Part (d)

First, solve equation (5), inserting (3) and data given values as follows:

Solving we obtain:

Similarly, solve (4) isolating as follows:

or

or

Repalcing values:

Solving we obtain:

This inconsistency is due to the fact that the reference system is non-inertial