Chapter 8.5, Problem 1CFU

To determine

To find: the situation that requires more force, assuming friction is zero.

Answer to Problem 1CFU

Lifting the object straight up

Explanation of Solution

Given information:

The given situations are as follows:

1. Pushing an object up to the top of an inclined.
2. Lifting an object straight up.

Calculation:

While lifting an object, the force exerted on the object such that the net force that acts on it is pointed in the upward direction. That is, the force required should be greater than its weight pointing downwards and has magnitude, $mg$ .

While pushing up an object to the top of an incline needs a force in the direction of slope such that the net force acting on the object accelerates the object up the slope. This force must be greater than the force component of weight which is parallel to the incline plane and points downwards the incline.

On resolving the weight into components, the magnitude of the component pointing down to the incline is $mg\sin \theta$ . The value of $\sin \theta$ for this case should be $0<\theta <1$ . Since $mg\sin \theta <mg$ for thus lifting an object straight up requires more force.