10. Exercises

A package with mass 300 kg is lifted vertically upwards. Find the tension in the cable which lifts the package, when the package,

a) accelerates upwards at 0.1 \displaystyle \text{m}{{\text{s}}^{-2}},

b) accelerates downwards at 0.2 \displaystyle \text{m}{{\text{s}}^{-2}},

c) travels upwards with a retardation of 0.1 \displaystyle \text{m}{{\text{s}}^{-2}}.

A car of mass 1 tonne travels along a horizontal road and brakes from 50 \displaystyle \text{m}{{\text{s}}^{-1}} to rest in a distance of 300 m. Find the magnitude of the braking force on the car.

A particle of mass 5 kg slides down a smooth plane, inclined at an angle of 30\displaystyle {}^\circ to the horizontal. Find the acceleration of the particle down the plane.

A particle of mass 6 kg starts from rest and accelerates uniformly. The resultant force on the particle has magnitude 15 N. Find the time taken to reach a speed of 10 \displaystyle \text{m}{{\text{s}}^{-1}}.

A block of mass 20 kg is pulled across a rough horizontal plane by a string, inclined at 30\displaystyle {}^\circ to the horizontal. If the tension in the string is 50 N and the acceleration produced is 0.5 \displaystyle \text{m}{{\text{s}}^{-2}} find the friction force on the block and the coefficient of friction.

A particle, of mass 12 kg slides down a rough slope inclined at 40\displaystyle {}^\circ to the horizontal. The coefficient of friction between the particle and the slope is 0.2. Find the acceleration of the particle.

A particle of mass 3 kg is pulled across a rough horizontal plane, by a string inclined at \displaystyle 30 {}^\circ to the horizontal by a force of 40 N. The coefficient of friction between the particle and the plane is 0.5. Find the acceleration of the particle.