Moments and centre of gravityEdexcel A-Level Physics: Subtopic test

1. 1
   A mechanic is loosening a stiff wheel nut using a spanner whose handle is 0.35 m long, measured from the centre of the nut to the point where she pushes. She applies a constant force of 120 N at the end of the handle.

   (a)

   The force is applied at right angles to the handle. Calculate the moment of the force about the centre of the nut.

   [1 mark]

   • A36 N m
   • B42 N m
   • C343 N m
   • D120 N m

   (b)

   She now pushes with the same 120 N force at the end of the handle, but at 30° to the handle instead of at right angles. What is the moment of the force about the nut?

   [1 mark]

   • A21 N m
   • B36 N m
   • C42 N m
   • D84 N m

   (c)

   Explain why a mechanic can loosen a stiff nut more easily using a longer spanner.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student wants to find the centre of gravity of an irregular piece of thick card. He makes a small hole near one edge, hangs the card freely from a pin through the hole, and hangs a plumb line from the same pin.

   (a)

   The card is left to hang freely until it stops moving. Where is the centre of gravity of the card?

   [1 mark]

   • AAt the centre of the hole
   • BOn the horizontal line through the pin
   • COn the vertical line through the pin, below the pin
   • DAt the lowest point on the edge of the card

   (b)

   The student draws the plumb line on the card, then repeats the procedure using a second hole. How does he now find the centre of gravity?

   [1 mark]

   • AThe two lines allow the mass of the card to be calculated
   • BThe centre of gravity is halfway along each plumb line
   • CThe two lines must be parallel, which shows the card is uniform
   • DThe centre of gravity is where the two lines cross

   (c)

   Explain why the card comes to rest with its centre of gravity vertically below the pin.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A uniform wooden beam of length 6.0 m and weight 400 N rests horizontally on two supports. Support A is at the left-hand end of the beam and support B is 5.0 m from A, so the right-hand end overhangs B by 1.0 m. A person of weight 900 N stands on the beam 1.5 m from A.

   (a)

   Use the principle of moments to calculate the upward force exerted on the beam by support B.

   [3 marks]

   (b)

   Calculate the force exerted by support A when the person is at their original position. The person then walks along the beam towards the right-hand end. Calculate how far beyond support B the person can stand before the beam is about to tip.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A delivery company is testing how tall boxes behave on a loading ramp. Each box is a uniform cuboid, and the ramp surface is rough enough that a box never slides, so a box can only tip by turning about its lower edge.

   (a)

   Explain, using centre of gravity and moments, why a tall narrow box tips over at a smaller ramp angle than a short wide box of the same material.

   [6 marks]

   (b)

   A uniform box is 0.60 m tall and 0.20 m wide. Calculate the largest angle to which the ramp can be tilted before this box tips. The ramp at the loading bay is inclined at 15°. Evaluate whether the box is safe on this ramp and suggest one change that would make it more stable.

   [6 marks]

   Total for question 4: 12 marks

End of questions