Edexcel International A Level Maths: Mechanics 1

Topic Questions

3.1 Forces

1
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2 marks

During a weightlifting competition, one of the competitors successfully lifts a barbell with a total mass of 135 kg and holds it stationary above her head with her elbows locked. State, with a reason, what the resultant force acting on the barbell is during the time that it is being held stationary above the weightlifter’s head.

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2
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3 marks

As part of an acrobatics display, one acrobat with a weight of 735 N is standing motionless on a horizontal floor. Another acrobat with a weight of 495 N is standing motionless on the first acrobat’s shoulders. State, with a reason, what the total normal reaction force exerted by the floor on the first acrobat is, and in what direction it is acting.

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3
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3 marks

Given that the particle in each of the following diagrams is stationary, work out the value of P:

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4
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3 marks

The following force diagram depicts a particle in equilibrium:

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By setting up and solving a pair of simultaneous equations, find the values of P and Q.

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5a
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2 marks

On a building site, a pallet of large stone blocks is being raised by a crane. The total weight of the pallet and blocks is 22000 N, and to make sure that the pallet remains level while it is being raised, the same tension, T, is maintained in each of the two lifting cables.  Other than the weight of the pallet and blocks, and the tension in the cables, all other influences on the motion of the pallet can be ignored.

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Given that the pallet is moving vertically upwards at a constant speed, work out the tension, T, in each cable.

5b
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2 marks

The tension in each cable is now increased by 1000 N.

Describe the resulting motion of the pallet, being sure to explain the physical reasoning behind your answer.

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6a
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3 marks

A truck with a total weight of 27000 N is moving along a horizontal level road. The truck’s engine provides a forward thrust of 13500 N. The total resistance is modelled by a constant force of 1700 N. All other forces acting on the truck may be ignored.

Modelling the truck as a particle, draw a force diagram to show the forces acting on the truck.

6b
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2 marks

Calculate the magnitude and direction of the resultant force acting on the truck.

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7a
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2 marks

A particle is acted upon by two forces, bold F subscript bold 1 bold space end subscript and space bold F subscript bold 2 given in vector form as

bold F subscript bold 1 equals left parenthesis 5 bold i plus 7 bold j right parenthesis space straight N space space space space space space space space space space space and space space space space space space space space space space space space bold F subscript bold 2 equals left parenthesis negative 3 bold i plus b bold j right parenthesis space straight N 

where b is a constant.

Find the angle between bold F subscript bold 1 and bold j.

7b
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3 marks

The resultant of bold F subscript bold 1 bold space end subscript and space bold F subscript bold 2 is bold R.

Given that bold R is parallel to the vector bold i minus 13 bold j, find the value of b.

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8a
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3 marks

A particle is acted upon by three forces, bold F subscript bold 1 bold comma bold space end subscript bold F subscript bold 2 bold space and bold space bold F subscript bold 3 given in vector form as

bold F subscript bold 1 equals left parenthesis negative 3 bold i plus 5 bold j right parenthesis space straight N space space space space space space space space space space space space bold F subscript bold 2 equals left parenthesis 12 bold i plus 2 bold j right parenthesis space straight N space space space space space space space space space bold space bold space bold F subscript bold 3 equals left parenthesis a bold i plus b bold j right parenthesis space straight N

where a space and space b are constants.

Given that the particle is in equilibrium,

Find the values of the constants a space and space b.

8b
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5 marks

The force bold F subscript bold 2 is now removed. The resultant of forces bold F subscript bold 1 bold space end subscript and space bold F subscript bold 3 is bold R.

Find the magnitude of  bold R and the angle that it makes with the horizontal.

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