Question

A block of mass 4.0 kg rests on a horizontal surface where the coefficient of kinetic friction between the two is 0.20. A string attached to the block is pulled horizontally, resulting in a 3.0-m/s ² acceleration by the block. Find the tension in the string. ( g = 9.80 m/s ²)

Answer 1

When two bodies in contact move with respect to each other, rubbing the surfaces in contact, the friction between them is called kinetic friction.

Kinetic friction

where is the coefficient of kinetic friction and N is the normal force.

Here the block will experience for forces,

1) The normal force N in the upward direction

2) The gravitational force F=Mg in the downward direction

3) The tension T , say in the right direction

4) The kinetic friction in the left direction

For vertical equilibrium,N=Mg

We have kinetic friction

As the block moves towards right with an acceleration a,

Total force on the block

  

=

=4×(3+ 0.2×9.8)

=19.84 N

The tension in the string is 19.84 N