Question

A 3.0 kg box slides on ice so smooth that the frictional force between the ice and box is zero. Air resistance is also zero. If the box is sliding at 4.0 m/s. How much force must be applied to the box to keep the box moving at 4.0 m/s?

• A. 3.0 N
• B. 29.4 N
• C. 0 N
• D. 4.0 N
• E. 39.2 N

Answer 1

The correct option is C 0 N

Given that frictional force and air resistance are zero .

Now Sir Newton's second law of motion states that the force applied on a body is directly proportional to the rate of change of momentum,

$F\propto dp/dt$

or $F=dp/dt=mdv/dt$ ,

where $dp=$ change in momentum ,

$dv=$ change in velocity ,

$dt=$ time interval

in the given case both mass $m$ and velocity of the box are constant for a time interval $dt$, so there is no change in momentum and hence the required force is zero .