Question

a mat of mass 1kg and length 1m is placed on the floor. one end of the mat is pulled with a constant speed of 1m/s towards the other end till the other end comes to motion (till the mat is reversed). how much force is required to do this?

Answer 1

 Nm²  I think the answer is 0.101971621 Nm². Because 1 kg = 0.101971621 N

Answer 2

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⟾ A mat is being pulled with a constant speed = v = 1m/s , so that the mass of the part of the mat is continuosly increasing.Hence here the mass is a variable.

The time required for bringing the entire mat in motion is given by

⟾ ∆ t = distance covered by the end / speed

2/1 = 2s

( Distance covered by the end = 1m + 1m = 2m)

From Newtons second law of motion,

F net = ∆p/∆t = ∆(mv) /∆t

Here v is constant, so we get

F net = v ∆m/∆t

Where, ∆m is the change of mass in ∆t time.

The change of mass in 2s is equal to entire mass of mat.

F net = (1m/s × (1kg) / 2s

= 1/2 N

⟾In the horizontal direction only one force is acting. Hence the required force is 1/2 N.