Question

When the momentum of an object increases with respect to time, what is true of the net force acting on it?

a. It is zero, because the net force is equal to the rate of change of the momentum.
b. It is zero, because the net force is equal to the product of the momentum and the time interval.
c. It is nonzero, because the net force is equal to the rate of change of the momentum.
d. It is nonzero, because the net force is equal to the product of the momentum and the time interval.

Answer 1

Answer:

C. It is nonzero, because the net force is equal to the rate of change of the momentum

Explanation:

Momentum of an object is given as;

P = mv = ft

f = mv/t

or f = P/t

where;

P is the momentum of the object

m is mass of the object

v is velocity of the object

f is the applied force on the object

t is time

From the given equation above; the net force acting on the object is equal to the rate of change of the momentum, thus it is non-zero.

Therefore, the correct option is "C"

C. It is nonzero, because the net force is equal to the rate of change of the momentum.

Answer 2

The net force acting on the object is non-zero, because the net force is equal to the rate of change of the momentum. Hence, option (c) is correct.

The problem is based on the impulse-momentum concept. As per the impulse -momentum concept, the magnitude of impulse produced by an object is equal to the change in momentum. Then the expression is,

$I = \Delta P$

here,

I is the magnitude of impulse. And its value is,

$I = F \times t$

t is the impact time or time interval.

F is the magnitude of net force.

$\Delta P$ is the change in momentum.

Solving as,

$I= \Delta P\\\\F \times t= \Delta P\\\\F = \dfrac{\Delta P}{t}$

Clearly, the net force is dependent of the change in momentum with respect to time. So, on increasing the momentum change with respect to time, the net force will also increase with non-zero value.

Thus, we can conclude that the net force acting on the object is non-zero, because the net force is equal to the rate of change of the momentum. Hence, option (c) is correct.

Learn more about the Impulse - momentum theorem here:

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