10. Exercises

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===Exercise 10.1===
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<div class="ovning">
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A package with mass 300 kg is lifted vertically upwards. Find the tension in the cable which lifts the package, when the package,
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a) accelerates upwards at 0.1 <math>\text{m}{{\text{s}}^{-2}}</math>,
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b) accelerates downwards at 0.2 <math>\text{m}{{\text{s}}^{-2}}</math>,
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c) travels upwards with a retardation of 0.1 <math>\text{m}{{\text{s}}^{-2}}</math>.
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</div>{{#NAVCONTENT:Answer a|Answer 10.1a|Answer b|Answer 10.1b|Answer c|Answer 10.1c|Solution a|Solution 10.1a|Solution b|Solution 10.1b|Solution c|Solution 10.1c}}
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===Exercise 10.2===
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<div class="ovning">
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A car of mass 1 tonne travels along a horizontal road and brakes from
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50 <math>\text{m}{{\text{s}}^{-1}}</math> to rest in a distance of 300 m. Find the magnitude of the braking force on the car.
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</div>{{#NAVCONTENT:Answer|Answer 10.2|Solution|Solution 10.2}}
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===Exercise 10.3===
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<div class="ovning">
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A particle of mass 5 kg slides down a smooth plane, inclined at an angle of 30<math>{}^\circ </math> to the horizontal. Find the acceleration of the particle down the plane.
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</div>{{#NAVCONTENT:Answer|Answer 10.3|Solution|Solution 10.3}}
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===Exercise 10.4===
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<div class="ovning">
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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 <math>\text{m}{{\text{s}}^{-1}}</math>.
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</div>{{#NAVCONTENT:Answer|Answer 10.4|Solution|Solution 10.4}}
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===Exercise 10.5===
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<div class="ovning">
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A block of mass 20 kg is pulled across a rough horizontal plane by a string, inclined at 30<math>{}^\circ </math> to the horizontal. If the tension in the string is 50 N and the acceleration produced is 0.5 <math>\text{m}{{\text{s}}^{-2}}</math> find the friction force on the block and the coefficient of friction.
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</div>{{#NAVCONTENT:Answer|Answer 10.5|Solution|Solution 10.5}}
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===Exercise 10.6===
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<div class="ovning">
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A particle, of mass 12 kg slides down a rough slope inclined at 40<math>{}^\circ </math> to the horizontal. The coefficient of friction between the particle and the slope is 0.2. Find the acceleration of the particle.
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</div>{{#NAVCONTENT:Answer|Answer 10.6|Solution|Solution 10.6}}
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===Exercise 10.7===
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<div class="ovning">
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A particle of mass 3 kg is pulled across a rough horizontal plane, by a string inclined at <math>30 {}^\circ </math> 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.
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</div>{{#NAVCONTENT:Answer|Answer 10.7|Solution|Solution 10.7}}

Current revision

       Theory          Exercises          Video      

Exercise 10.1

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}}.

Answer a
Answer 10.1a
Answer b
Answer 10.1b
Answer c
Answer 10.1c
Solution a
Solution 10.1a
Solution b
Solution 10.1b
Solution c
Solution 10.1c

Exercise 10.2

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.


Answer
Answer 10.2
Solution
Solution 10.2


Exercise 10.3

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.


Answer
Answer 10.3
Solution
Solution 10.3

Exercise 10.4

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}}.


Answer
Answer 10.4
Solution
Solution 10.4

Exercise 10.5

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.

Answer
Answer 10.5
Solution
Solution 10.5

Exercise 10.6

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.

Answer
Answer 10.6
Solution
Solution 10.6


Exercise 10.7

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.

Answer
Answer 10.7
Solution
Solution 10.7
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