Answer to Question #264291 in Mechanics | Relativity for john

Question

2. A 12.6 kg block is connected to a 28.0 kg of bucket full of steel ball by a

string through a frictionless pulley as in the figure below. When the block is in

motion, the kinetic friction force on the surface of the table is 8.96 N.

a. Draw a free-body diagram for both block and bucket.

b. Calculate the acceleration of both block and bucket. Give your

answer in two decimal places.

Answer 1

Explanations & Calculations

a)

b)

• The acceleration of both bucket and block is the same as they are connected by the same thread across a simple pully.
• Applying Newton's second law to both objects in their acceleration directions help finding the acceleration.
• Motion is: bucket moves down and as a result, the block moved horizontally on the table (say, to the right)

$\qquad\qquad \begin{aligned} \small \to F&=\small ma\\ \small T-f&=\small ma\cdots(1)\\ \\ \small \downarrow F&=\small ma\\ \small Mg-T&=\small Ma\cdots(2)\\ \\ (1)+(2)\\ \\ \small Mg-f&=\small Ma+ma\\ \small a&=\small \frac{Mg-f}{(M+m)}\\ &=\small \frac{28\times9.8-8.96}{(28+12.6)}\\ &=\small 6.54\,ms^{-2} \end{aligned}$