Test A - Extra Lessons
Test A - Extra Lessons
Test A - Extra Lessons
(b) The pressure p due to a liquid of density ρdepends on the depth h, gravity g and density ρ
of the liquid.
(i) Deduce the relationship. [4]
(ii) Use this deduced expression to determine the derived units of pressure. Explain your
working. [5]
(ii) In the following list, give all the scalar and vector quantities.
(d) A stone is thrown with a horizontal velocity of 20 m s–1 from the top of a cliff 15 m high.
The path of the stone is shown in Fig. 1.1.
Fig. 1.1
Air resistance is negligible.
F = 6πDRv
(i) Show that the SI base units of the quantity D are kg m-1s-1. [3]
(ii) A raindrop of radius 1.5 mm falls vertically in air at a velocity of 3.7 ms-1. The value of D for air is
6.6 × 10-4 kg m-1s-1. The density of water is 1000 kgm-3.
Calculate
1. the magnitude of the frictional force F, [3]
2. the acceleration of the raindrop. [3]
(b) The variation with time t of the speed v of the raindrop in (a) is shown in Fig. 2.1.
Fig. 2.1
(i) State the variation with time of the acceleration of the raindrop. [3]
(ii) A second raindrop has a radius that is smaller than that given in (a). On a copy of Fig. 2.1, sketch
the variation of speed with time for this second raindrop. [2]
3 A shopping trolley and its contents have a total mass of 42 kg. The trolley is being pushed
along a horizontal surface at a speed of 1.2 m s–1. When the trolley is released, it travels a
distance of 1.9 m before coming to rest.
(a) Assuming that the total force opposing the motion of the trolley is constant,
(i) calculate the deceleration of the trolley, [2]
(ii) show that the total force opposing the motion of the trolley is 16 N. [1]
(b) Using the answer in (a)(ii), calculate the power required to overcome the total force
opposing the motion of the trolley at a speed of 1.2 ms-1. ]2]
(c) The trolley now moves down a straight slope that is inclined at an angle of 2.8° to the
horizontal, as shown in Fig. 3.1.
Fig. 3.1
[2]
(ii) the time for the trolley to travel from rest a distance of 3.5 m along the length of the slope.[4]
(d) Use your answer to (c)(ii) to explain why, for safety reasons, the slope is not made any
steeper. [1]
4 An experiment is conducted on the surface of the planet Mars.
A sphere of mass 0.78 kg is projected almost vertically upwards from the surface of the
planet. The variation with time t of the vertical velocity v in the upward direction is shown in
Fig. 4.1.
Fig. 4.1
The sphere lands on a small hill at time t = 4.0 s.
(a) State the time t at which the sphere reaches its maximum height above the planet’s surface.
Explain your answer [2]
(b) Determine the vertical height above the point of projection at which the sphere finally comes
to rest on the hill. [3]
(c) Calculate, for the first 3.5 s of the motion of the sphere,
(i) the change in momentum of the sphere, [2]
(ii) the force acting on the sphere. [2]