Chapter 8, Problem 97A

(a)

To determine

The load that is easier to lift.

Answer to Problem 97A

The same upward force is required to lift each load.

Explanation of Solution

Given info:

The length of the lumber is $2.44\text{ m}$ .

The length of the lumber after cutting it into two pieces is $1.22\text{ m}$ .

Formula used:

The force is given as,

  $f=ma$

Calculation:

The minimum force required to lift an object is equal to its weight.

The lumber is cut into two loads of same lengths. Then the masses and weights of the loads are same. So, the same force is required to lift each load.

Hence, the same upward force is required to lift each load.

Conclusion:

Thus, the same upward force is required to lift each load.

(b)

To determine

The load that is easier to keep from rotating.

Answer to Problem 97A

The longer lumber would be easier to keep from rotating.

Explanation of Solution

Given:

The length of the lumber is $2.44\text{ m}$ .

The length of the lumber after cut into two pieces is $1.22\text{ m}$ .

Formula used:

Torque is given as,

  $\tau =rF\sin \theta$

Calculation:

Consider the lumber rotates about the passing through the person’s shoulder.

The expression for the torque due to gravitational force is the product of the lumber’s weight and half of the length of the lumber.

$\tau =F_{\text{g}}\left(\frac{l}{2}\right)$

The moment of inertia for the longer lumber is greater when compared to shorter lumber. The lesser force is required to produce torque in the longer lumber. So, when compared to the shorter lumber the longer lumber would be easier to keep from rotating

Conclusion:

Thus, the longer lumber would be easier to keep from rotating.