Q. 35

Expert-verified
Found in: Page 179

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# The coefficient of static friction is between the two blocks in FIGURE . The coefficient of kinetic friction between the lower block and the floor is . Forcecauses both blocks to cross a distance of , starting from rest. What is the least amount of time in which this motion can be completed without the top block sliding on the lower block?

The smallest amount amount of your time within which the motion will be completed is . .

See the step by step solution

## Step 1: Upper block free diagram

The free body diagram of the upper block is provided within the below figure.

In the above figure, is that the force applied to the upper block, is that the mass of upper block, is that the burden of the upper block, is that the acceleration due to gravity, is that the traditional force on the upper block, and is that the force of static friction between the upper and lower bocks.

## Step 2: Upper block

For upper block, the standard force balances its weight . So, the net force on the upper block along vertical direction is capable zero. Thus,Thus, the net force on the upper block along horizontal direction is,As the upper block remains on the lower block, the web force thereon is capable zero. So, the above equation is also rearranged as follows:

The static friction are often expressed in terms of coefficient of static friction and so the traditional force. So, the static friction force between the blocks is,

## Step 3: Free-body diagram

Similarly, the free body diagram of the lower block is shown within the below figure.

In the above figure is that the kinetic friction force between the lower block and thus the ground , is that the mass of the lower block, is that the traditional force on the lower block, and is that the total weight of lower and upper blocks.

## Step 4: Kinetic friction

For the lower block, the normal force balances the weight . Thus,The net force on the lower block along the horizontal direction is,The kinetic friction is expressed in terms of coefficient of kinetic friction and so the conventional force. So, the kinetic friction force between the lower block and floor is,Replace with .The net force of the lower block may additionally be expressed in terms of its mass and acceleration as follows:Here, is that the acceleration of the system.Replace with with and with in and rearrange the resulting equation for .

Substitute for for , for for and for

Thus, the acceleration of the system is

## Step 5: System of blocks

The time taken for the system of blocks to cover the given distance is calculated by using the next kinematic equation.Here, is that the initial sped of the system of blocks.Substitute for , 0 for , and for , and solve for .

Round off to significant figures, the time taken for the system of blocks to cover the given distance is .