Question

Question: Because the change of the momentum is equal to the net impulse, the relationship of momentum itself to the net force is somewhat indirect, as can be seen in this question. An object is initially moving in the + x direction with a magnitude of momentum P , with a net force of magnitude F acting on the object in either the + x or - x direction. After a very short time, say whether the magnitude of the momentum increases, decreases, or stays the same in each of the following situations:

a) the net force acts in the + x direction and is F constant.

b) the net force acts in the + x direction and is F increasing.

c) the net force acts in the + x direction and is F decreasing.

d) the net force acts in the - x direction and is F constant.

e) the net force acts in the - x direction and is F increasing.

f) the net force acts in the - x direction and is F decreasing.

Short answer

Answer

The magnitude of the momentum of the object in these cases a) stays the same, b) increases, c) decreases, d) stays the same, e) increases, and f) decreases.

Step-by-step solution

 Step 1: Identification of the given data

The given data can be listed below as,

• The object is moving in the + X direction.
• The magnitude of the momentum of the object is P.
• The net force of magnitude acting on the object isF.

Significance of Newton’s second law for the momentum 

This law states that the rate of the change of momentum of an object is mainly directly proportional to the force applied, and it also takes place in the acting force’s direction.

The second law of Newton can be expressed as F = ma, where F is the acting force and is the product of the mass and acceleration. The changes in the force and its direction give the changes in the momentum for the force.

Determination of the magnitude of the momentum 

a) From Newton’s second law, the magnitude of the momentum stays the same as the net force has not changed.

b) From Newton’s second law, the magnitude of the momentum of the object will increase as the force F increases.

c) From Newton’s second law, the magnitude of the momentum of the object will decrease as the net force is decreasing.

d) From Newton’s second law, the magnitude of the momentum of the object stays the same as the net force has not changed.

e) From Newton’s second law, the magnitude of the momentum of the object will increase as the force increases.

f) From Newton’s second law, the magnitude of the momentum of the object will decrease as the net force is decreasing.

Thus, the magnitude of the momentum of the object in these cases a) stays the same, b) increases, c) decreases, d) stays the same, e) increases, and f) decreases.