Question 1 (Marks: 25)
(a) A cyclist is initially travelling in the positive
x direction. She makes a 180° turn with
radius r, turning to the left (or anticlockwise
viewed from above). Her speed is constant at
v throughout. Using i, j, k notation, write
(i) her velocity halfway through the turn
(ii) her acceleration halfway through the turn
(iii) her average acceleration during the turn.
For (iii), show your working.
In all of them, be careful of your notation.
A rectangular crate of mass 35 kg is being unloaded from an aeroplane, as shown in the sketch.
Inside the plane, it is pushed 2.0 metres across a rough horizontal floor to the door of the aircraft at
a constant speed of 1.0 m.s-1.
(b) Draw a free body diagram showing the forces acting on the crate while it moves across the
horizontal floor. (The coefficient of friction is not negligible.)
(c) What is the acceleration of the crate while it is being pushed across the horizontal floor of the
(d) The crate is pushed out the cargo door of the aeroplane, with an initial velocity of 1.0 m.s-1
down the ramp, onto a rough ramp joining the cargo door to the ground. It then slides down
the ramp. The ramp makes an angle of 30 degrees to the horizontal, and the coefficient of
kinetic friction between the ramp and the crate is 0.40. The height of the cargo door above the
ground is 10.0 m.
(i) Draw a free body diagram showing all the forces acting on the crate while it is on the
(ii) Determine the magnitude and the direction of acceleration of the box while it is sliding
down the ramp
(iii) What is the speed of the crate just as it reaches the ground?
(iv) How much potential energy does the crate lose in travelling down the ramp from the
cargo door to the ground?
(v) How much work is done against friction during the time the crate is on the ramp?