3. Exercises

From Mechanics

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===Exercise 3.2===
===Exercise 3.2===
<div class="ovning">
<div class="ovning">
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A sphere, of mass 20 kg, is supported by a single vertical cable. Find the tension in the cable.
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A particle of mass 2.5 kg is hanging, in equilibrium from a spring. Calculate the tension in the spring.
</div>{{#NAVCONTENT:Answer|Answer 3.2|Solution|Solution 3.2}}
</div>{{#NAVCONTENT:Answer|Answer 3.2|Solution|Solution 3.2}}
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The diagram shows two masses and two strings that are suspended from a fixed point.
The diagram shows two masses and two strings that are suspended from a fixed point.
Find the tension in each string.
Find the tension in each string.
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</div>{{#NAVCONTENT:Answer|Answer 3.3|Solution|Solution 3.3}}
</div>{{#NAVCONTENT:Answer|Answer 3.3|Solution|Solution 3.3}}
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===Exercise 3.4===
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<div class="ovning">
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[[Image:E3.4.GIF]]
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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.
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</div>{{#NAVCONTENT:Answer|Answer 3.4}}
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===Exercise 3.5===
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<div class="ovning">
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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.
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a) Draw diagrams to show the forces on each book.
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b) Calculate the magnitude of the normal reaction force acting on the top book.
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c) Calculate the magnitude of the normal reaction forces acting on the bottom book.
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</div>{{#NAVCONTENT:Answer a|Answer 3.5a|Answer b|Answer 3.5b|Answer c|Answer 3.5c|Solution b|Solution 3.5b|Solution c|Solution 3.5c}}
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===Exercise 3.6===
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<div class="ovning">
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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
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a) its lowest point,
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b) its highest point,
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c) between its highest and lowest points.
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</div>{{#NAVCONTENT:Answer a|Answer 3.6a|Answer b|Answer 3.6b|Answer c|Answer 3.6c}}
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===Exercise 3.7===
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<div class="ovning">
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A sledge slides down a slope. Draw a diagram to show the forces acting on the sledge.
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</div>{{#NAVCONTENT:Answer|Answer 3.7}}
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===Exercise 3.8===
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<div class="ovning">
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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.
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</div>{{#NAVCONTENT:Diagram|Diagram3.8|Answer|Answer 3.8|Solution|Solution 3.8}}
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===Exercise 3.9===
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<div class="ovning">
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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.
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[[Image:E3.9.GIF]]
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a) Calculate the magnitude of the normal reaction force acting on the box.
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b) What is the magnitude of the friction force on the box if <math>P=760\text{ N}</math>.
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Explain your answer.
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c) Calculate the magnitude of the resultant force on the box if <math>P=1000\text{ N}</math>.
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</div>{{#NAVCONTENT:Answer a|Answer 3.9a|Answer b|Answer 3.9b|Answer c|Answer 3.9c|Solution a|Solution 3.9a|Solution b|Solution 3.9b|Solution c|Solution 3.9c}}
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===Exercise 3.10===
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<div class="ovning">
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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 .
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[[Image:E3.10.GIF]]
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a) Find the tension in the string.
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b) Find the normal reaction force on the block.
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c) Find the magnitude of the friction force.
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d) Find an inequality that <math>\mu </math> must satisfy.
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</div>{{#NAVCONTENT:Answer a|Answer 3.10a|Answer b|Answer 3.10b|Answer c|Answer 3.10c|Answer d|Answer 3.10d|Solution a|Solution 3.10a|Solution b|Solution 3.10b|Solution c|Solution 3.10c|Solution d|Solution 3.10d}}
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===Exercise 3.11===
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<div class="ovning">
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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.
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[[Image:E3.11.GIF]]
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a) Find the tension in the right hand string.
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b) Find the tension in the left hand string.
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c) Find an inequality that the coefficient of friction between the block and the surface must satisfy.
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</div>{{#NAVCONTENT:Answer a|Answer 3.11a|Answer b|Answer 3.11b|Answer c|Answer 3.11c|Solution a|Solution 3.11a|Solution b|Solution 3.11b|Solution c|Solution 3.11c}}
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===Exercise 3.12===
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<div class="ovning">
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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.
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What happens to the sledge if;
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a) P = 40 N,
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b) P = 30 N,
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c) P = 35.28 N ?
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</div>{{#NAVCONTENT:Answer a|Answer 3.12a|Answer b|Answer 3.12b|Answer c|Answer 3.12c|Solution |Solution }}
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===Exercise 3.13===
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<div class="ovning">
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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.
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a) Draw a diagram to show the forces acting on the tank.
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b) Find the magnitude of the friction force acting on the tank.
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c) Find the magnitude of the resultant force on the tank.
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</div>{{#NAVCONTENT:Answer a|Answer 3.13a|Answer b|Answer 3.13b|Answer c|Answer 3.13c|Solution b and c|Solution 3.13bc}}

Current revision

       Theory          Exercises          Video      


Exercise 3.1

A sphere, of mass 20 kg, is supported by a single vertical cable. Find the tension in the cable.

Answer
Answer 3.1
Solution
Solution 3.1


Exercise 3.2

A particle of mass 2.5 kg is hanging, in equilibrium from a spring. Calculate the tension in the spring.

Answer
Answer 3.2
Solution
Solution 3.2


Exercise 3.3

Image:E3.3.GIF

The diagram shows two masses and two strings that are suspended from a fixed point. Find the tension in each string.

Answer
Answer 3.3
Solution
Solution 3.3


Exercise 3.4

Image:E3.4.GIF

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.

Answer
Answer 3.4


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.

Answer a
Answer 3.5a
Answer b
Answer 3.5b
Answer c
Answer 3.5c
Solution b
Solution 3.5b
Solution c
Solution 3.5c


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.

Answer a
Answer 3.6a
Answer b
Answer 3.6b
Answer c
Answer 3.6c


Exercise 3.7

A sledge slides down a slope. Draw a diagram to show the forces acting on the sledge.

Answer
Answer 3.7


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.

Diagram
Diagram3.8
Answer
Answer 3.8
Solution
Solution 3.8


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.


Image:E3.9.GIF

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}.

Answer a
Answer 3.9a
Answer b
Answer 3.9b
Answer c
Answer 3.9c
Solution a
Solution 3.9a
Solution b
Solution 3.9b
Solution c
Solution 3.9c


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 .


Image:E3.10.GIF

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.


Answer a
Answer 3.10a
Answer b
Answer 3.10b
Answer c
Answer 3.10c
Answer d
Answer 3.10d
Solution a
Solution 3.10a
Solution b
Solution 3.10b
Solution c
Solution 3.10c
Solution d
Solution 3.10d


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.


Image:E3.11.GIF

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.

Answer a
Answer 3.11a
Answer b
Answer 3.11b
Answer c
Answer 3.11c
Solution a
Solution 3.11a
Solution b
Solution 3.11b
Solution c
Solution 3.11c


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 ?


Answer a
Answer 3.12a
Answer b
Answer 3.12b
Answer c
Answer 3.12c
Solution
Solution


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.


Answer a
Answer 3.13a
Answer b
Answer 3.13b
Answer c
Answer 3.13c
Solution b and c
Solution 3.13bc
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