3. Exercises
From Mechanics
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Exercise 3.1
A sphere, of mass 20 kg, is supported by a single vertical cable. Find the tension in the cable.
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Exercise 3.2
A particle of mass 2.5 kg is hanging, in equilibrium from a spring. Calculate the tension in the spring.
Exercise 3.3
The diagram shows two masses and two strings that are suspended from a fixed point. Find the tension in each string.
Exercise 3.4
A plank leans against the back of a lorry, as shown in the diagram. Draw a diagram to show the forces acting on the plank.
Exercise 3.5
Two books are placed, one on top of each other on a horizontal surface. The top book has mass 1.2 kg and the lower book has mass 1.8 kg.
a) Draw diagrams to show the forces on each book.
b) Calculate the magnitude of the normal reaction force acting on the top book.
c) Calculate the magnitude of the normal reaction forces acting on the bottom book.
Exercise 3.6
A simple pendulum consists of a small metal sphere attached to a length of string. The sphere then swings in a vertical plane, describing a circular arc. Draw a diagram to show the forces acting on the sphere when it is at
a) its lowest point,
b) its highest point,
c) between its highest and lowest points.
Exercise 3.7
A sledge slides down a slope. Draw a diagram to show the forces acting on the sledge.
Exercise 3.8
Three boxes have masses of 5 kg, 12 kg and 10 kg. They are stacked on a horizontal surface with the 12 kg box at the bottom. Draw a diagram to show the forces acting on the 12kg box and calculate the magnitude of each of these forces.
Exercise 3.9
A box, of mass 200 kg, is on a rough, horizontal surface. A horizontal force of magnitude P N acts on the box as shown in the diagram. The coefficient of friction between the surface and the box is 0.4.
a) Calculate the magnitude of the normal reaction force acting on the box.
b) What is the magnitude of the friction force on the box if \displaystyle P=760\text{ N}.
Explain your answer.
c) Calculate the magnitude of the resultant force on the box if \displaystyle P=1000\text{ N}.
Exercise 3.10
The diagram shows a block of mass 12 kg that is connected by a light string to a weight of mass 8 kg. The system remains at rest, with the block on a horizontal surface. The coefficient of friction between the block and the horizontal surface is .
a) Find the tension in the string.
b) Find the normal reaction force on the block.
c) Find the magnitude of the friction force.
d) Find an inequality that \displaystyle \mu must satisfy.
Exercise 3.11
The diagram shows a system, in which two weights are attached by light strings to a block that is at rest on a rough horizontal surface.
a) Find the tension in the right hand string.
b) Find the tension in the left hand string.
c) Find an inequality that the coefficient of friction between the block and the surface must satisfy.
Exercise 3.12
A sledge has mass 12 kg. It rests on a horizontal surface. The coefficient of friction between the sledge and the ground is 0.3. A horizontal force of P N acts on the sledge. What happens to the sledge if;
a) P = 40 N,
b) P = 30 N,
c) P = 35.28 N ?
Exercise 3.13
A tank has mass 800 kg. It is pulled along a horizontal surface by a rope attached to a tractor. The coefficient of friction between the tank and the ground is 0.6. The rope exerts a horizontal force of magnitude 5000 N on the tank.
a) Draw a diagram to show the forces acting on the tank.
b) Find the magnitude of the friction force acting on the tank.
c) Find the magnitude of the resultant force on the tank.
