GCSE Questions: Forces

Q8. The diagram shows a boat floating on the sea. The boat is stationary.

(a) Here is part of the free body diagram for the boat.

(i) Complete the free body diagram for the boat.

The first mark was given for drawing an arrow of equal size pointing vertically upwards - (see diagram) - the second mark went for labelling the upwards force as 'upthrust'.

Any horizontal arrows you drew were ignoried if they were equal and opposite in size but unequal length ones that did not cancel each other out lost you the mark.

Only 'upthrust' got you the marks for labelling the arrow - 'buoyancy' or '25 kN' were ignored. It is very important that you use keywords specified in the syllabus when you construct your answers - otherwise you will throw marks away.

[2 marks]

(ii) Calculate the mass of the boat given that the gravitational field strength = 9.8 N/kg.

Give your answer to two significant figures.

Measuring the line on the free body diagram, you find that it is 5cm long - it therefore represents a force of 25 kN (as 1 cm = 5 kN).

The boat weighs 25 x 10³ N

weight = mass x gravitational field strength

w = mg

m = w/g

m = 25 x 10³/9.8

m = 2,551 kg

m = 2,600kg (to 2 sig figs)

[4 marks]

(b) When the boat propeller pushes water backwards, the boat moves forwards. The force on the water causes an equal and opposite force to act on the boat.

Which law is this an example of?

Newton's Third Law (of motion)

[1 mark]

(c) The diagram below shows the boat towing a small dinghy.

The tension force in the tow rope causes a horizontal force forwards and a vertical force upwards on the dinghy.

horizontal force forwards = 150 N

vertical force upwards = 50 N

Here is a piece of graphpaper. Use it to draw a vector diagram, to scale, in order to determine the magnitude of the tension force in the tow rope, and the direction of the force this causes on the dinghy.

You have to draw a scale diagram - 150 and 50 are needed - but the grid on the graph paper is 8 by 8

one square being 10 will allow a maximum size of 80 - not enough...

one square being 20 will allow a maximum size of 160 so that will be okay!

It is sensible to choose 1 cm = 10 N (or one full square division of graph paper represents 20N). That is making your scale diagram as large as possible

You have to draw the vectors very carefully and construct the resultant vector.

See the graph paper.

You got 1 mark for drawing the vertical force (50 N) and horizontal force (150 N) to the same scale

You got 1 mark for drawing in the resultant tension force in the correct direction. you need to put in arrowheads to get this mark!

The resultant line is 15.8 cm long - so the force it represents is 158 N. You got 1 mark for this (they allowed you to be out a bit - answer must be in the range 156 - 160 N)

The angle is always measured anticlockwise from the horizontal - it is 18^o (they allowed you to be out a bit - but answer must be in the range 18^o - 20^o )

We can calculate the values to check our drawing:

Using Pythagoras

x² = 50² + 150²

x² = 2500 + 22500 =25000

x = √25000 = 158.11

Using trig

tan θ = ⁵⁰/150 = ¹/3

θ = tan^-1 0.333 = 18.43^o

[4 marks]

[11 Marks TOTAL]