A block of mass slides along a smooth horizontal surface while a horizontal force…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A block of mass

2\,\text{kg}

slides along a smooth horizontal surface while a horizontal force acts on it. The variation of the force with displacement is such that: • From

x = 0

x = 4\,\text{m}

, the force increases uniformly from

0\,\text{N}

20\,\text{N}

. • From

x = 4\,\text{m}

x = 8\,\text{m}

, the force decreases uniformly from

20\,\text{N}

-10\,\text{N}

(opposite to the direction of motion). Initially the block is moving in the positive x-direction with a speed of

1\,\text{m\,s}^{-1}

. (i) Compute the work done by the force in the first

4\,\text{m}

of travel. (ii) Compute the work done by the force from

x = 4\,\text{m}

x = 8\,\text{m}

. (iii) Determine the net work done over the entire

0

8\,\text{m}

interval. (iv) Using the work–energy principle, calculate the speed of the block after it has travelled

8\,\text{m}