Question

A truck of mass \[500kg\] moving with constant speed \[10m/s\] . If sand is dropped into the truck at the constant rate of \[10kg/min\] , the force required to maintain the motion with constant velocity is:
(A) $\dfrac{5}{3}N$
(B) $\dfrac{5}{4}N$
(C) $\dfrac{7}{5}N$
(D) $\dfrac{3}{2}N$

Answer 1

Hint: Force is the rate of change of momentum, according to Newtons' second law. At speeds less than the speed of light, the mass of the object remains constant. So, we can also write force as the product of mass and acceleration.


Complete step by step solution:
Let us first write the given information in the question.
$m = 500kg,speed = 10m/s$,
Rate of dropping the send = $10kg/\min = \dfrac{1}{6}kg/\sec $
We have to find the force required to maintain the motion with constant velocity.
Here, speed is constant; it means the acceleration will be zero. Hence, the net force will also be zero.
Rate of dropping send id $\dfrac{1}{6}kg/\sec $, that is, after one-second mass will increase by $\dfrac{1}{6}kg$.
From Newton's second law, force is the rate of change of momentum.
$F = \dfrac{{d(momentum)}}{{dt}} = \dfrac{{d(mv)}}{{dt}}$
Let us substitute the values, when time is \[1sec\].
$F = \dfrac{{\dfrac{1}{6} \times 10}}{1} = \dfrac{5}{3}N$
Therefore, the force required to maintain the motion with constant velocity is $\dfrac{5}{3}N$.
Hence, the correct option is (A) $\dfrac{5}{3}N$.

Note:
Whenever an object is moving with some acceleration, a force must be acting on it.
When speed is constant, acceleration will be zero. Hence, the net force acting will be zero.
Net force zero does not mean that there is no force acting on the object. Instead, it means all the forces balance each other.
Speed and velocity are scalars and vector quantities respectively. Even if speed is constant, velocity can change if direction changes.