MCD4160 Physics for Engineering
PRACTICE TEST Duration: 50
minutes. Closed Book.
FORMULAE AND DATA
ΣF = ma a = v2/R (uniform circular motion) g = 9.8 N/kg
F(x) = − dU
dx
W = F.d = F d cosθ K = ½ m v2 ∆K = W
x cm
∑mi x i
= i
∑mi

vcm
∑mi vi
= i
∑mi
ΣF = dp
dt
p = mv

Στ = dL L = Iω L = r x p I = ∑m r 2
dt
x = X cos ωt ω = (k / m) 1/2 SHM.

F = GMm
r 2
i

T2 ∝ r3
REarth =6.38 × 106 m MEarth = 5.98 × 1024 kg G = 6.67 × 10-11 Nm2kg-2
QUESTION 1 (2 + 2 = 4 marks)
A small car has a dead battery and a large truck is pushing the car. The mass of the truck is
larger than the mass of the car.
(a) Draw the body force digram for the all forces acting on the car while being pushed by
the truck, you may ignore the air resistance. Use FAB to indicate the force ac\tining by object A
on object B.
(b) Which of the following statements is true?

A. The truck exerts a force on the car, but the car doesn’t exert a force on the truck.
B. The truck exerts a larger force on the car than the car exerts on the truck.
C. The truck exerts the same amount of force on the car as the car exerts on the truck.
D. The car exerts a larger force on the truck than the truck exerts on the car
QUESTION 2 (3 + 2 = 5 marks)
Simone (mass = 65 kg) and Justine (mass = 80 kg) are ice-skating. Justine is skating at 5 m s-1, and
Simone is stationary, as shown in the figure below. Justine collides with Simone, they push off each
other, and Simone moves off with a speed of 8 m s-1.
(a) Determine the Speed and direction of Justine after the collision? Show your working.
(b) Determine the change in kinetic energy of the system.
V= 5 m s-1
Simone Justine
2

0
0 2 4 6
x (cm)
QUESTION 3 (3 + 2= 5 marks)

A person of mass 75 kg stands at the centre of a rotating merry-go-round platform of radius 3.0 m and
moment of inertia 920 kg m2. The platform rotates without friction with angular velocity 2.0 rad s-1. The
person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.

(b) Calculate the rotational kinetic energy of the system of the platform plus person before
and after the person’s walk.
QUESTION 4 (4 + 2 = 6 marks)

The figure below shows the potential energy of a 10 g particle with respect to its position.
(a) In the axes provided below draw a force versus position graph from x = 0 to x = 8 cm.
Indicate the appropriate numbers on the force axis in your graph.
(b) How much work does the force do as the particle moves from x = 2 cm to x = 6 cm? Show
your working.
x (cm)
F (N)
2 4 6 8
8
U (J)
8
6

4
10
QUESTION 5 (3 + 2 = 5 marks)

A uniform rod of mass M and length L can pivot freely (with negligible friction) about a hinge attached to
a wall as shown below. The rod is held horizontally and then released. The moment of inertia of a long
uniform rod of mass M and length L with respect to the axis passing through the end is (1/3) ML2.
(a) At the moment of release, determine the angular acceleration of the rod. Show your
working.
(b) At the moment of release, what is the linear acceleration of the tip of the rod?
QUESTION 6 (4 marks)

Determine the time it takes for a satellite to orbit the earth in a circular “near-Earth” orbit A “near-Earth”
orbit is one at a height above the surface of the Earth which is very small compared to the radius of the
Earth.
END OF TEST
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