2. Exercises

A man, of mass 75 kg, stands on a horizontal surface. Assume that the man has two points of contact with the ground.

a) Draw a diagram to show the forces acting on the man.

b) Calculate the magnitude of each of these forces.

An aeroplane circles an airport at a constant speed. Are the forces acting on the aeroplane in equilibrium? Explain your answer.

A helicopter, of mass 800 kg, is rising at a constant rate.

a) Are the forces acting on the helicopter in equilibrium?

b) Calculate the magnitude of the vertical lift force on the helicopter.

Calculate the magnitude of the force that gravity exerts on each of the following objects.

a) A car of mass 1250 kg.

b) A table tennis ball of mass 4 grams.

c) A lorry of mass 4.2 tonnes.

The weight of a body is 441 N. Calculate the mass of the body.

A satellite, of mass 300 kg, orbits the earth at a height of 7000 km above the surface of the earth. Calculate the magnitude of the gravitational attraction that acts on the satellite.

The mass of the moon is \displaystyle \text{7}\textrm{.}\text{38}\times \text{1}{{0}^{22}} kg and the radius of the moon is \displaystyle \text{1}\textrm{.}\text{73}\times \text{1}{{0}^{6}} m. Determine the acceleration due to gravity on the moon, by considering the force that the moon exerts on a particle of mass 1 kg on its surface.

A planet has a mass of \displaystyle \text{5}\times \text{1}{{0}^{20}} kg and on this planet the acceleration due to gravity is 3.2 ms-1. Determine the radius of the planet.

A man, of mass 80 kg, climbs 5000 m to the top of a mountain.

a) Use the Universal Law of Gravitation to calculate the gravitational attraction on the man.

b) Compare your answer to part (a) with the result given by using mg.

The mass of Mars is \displaystyle \text{6}\textrm{.}\text{42}\times \text{1}{{0}^{23}} kg and the radius of the planet is 3400 km. What is the acceleration due to gravity on Mars?