CAIE A-Level Physics 3.1 Momentum and Newton’s Laws of Motion

Practise applying Newton’s laws, momentum and force relationships with vectors, units, free-body reasoning, graphs and action-reaction pairs.

Exam points

Explain mass, force, momentum, weight and Newtonian interaction using correct scalar/vector directions, units and free-body reasoning.
Apply F=ma, p=mv and F=Δp/Δt to solve mechanics problems and interpret resultant forces.
Identify Newton’s-law force pairs and distinguish weight, mass, momentum and resistive effects in a physical system.

Covered syllabus points

3.1.1—Mass is the property of an object that resists change in motion 3.1.2—F = ma and solve problems using it, understanding that acceleration and 3.1.3—Linear momentum as the product of mass and velocity 3.1.4—Force as rate of change of momentum 3.1.5—Each of Newton’s laws of motion 3.1.6—The concept of weight as the effect of a gravitational field on a mass and

[Maximum number: 3]

(a)

State what is meant by the mass of a body.

[ 1 ]

(b)

Two blocks travel directly towards each other along a horizontal, frictionless surface. The blocks collide, as illustrated in Fig. 3.1.

Fig. 3.1

Block A has mass 3 M and block B has mass M.
Before the collision, block A moves to the right with speed $0.40 \mathrm{~ms}^{-1}$ and block B moves to the left with speed $0.25 \mathrm{~ms}^{-1}$ .
After the collision, block A moves to the right with speed $0.20 \mathrm{~m} \mathrm{~s}^{-1}$ and block B moves to the right with speed v.

[ 2 ]

(i)

Use Newton's third law to explain why, during the collision, the change in momentum of block A is equal and opposite to the change in momentum of block B.

[ 2 ]

[Maximum number: 4]

A child on a sledge slides down a steep hill and then travels in a straight line up an ice-covered slope, as illustrated in Fig. 3.1.

Fig. 3.1 (not to scale)

The sledge passes point A with speed $18 \mathrm{~ms}^{-1}$ at time t=0 and then comes to rest at point B. The child applies a brake to the sledge at point B. The brake does not keep the sledge stationary and it immediately slides back down the slope towards A .

The variation with time t of the velocity v of the sledge from t=0 to $t=24 \mathrm{~s}$ is shown in Fig. 3.2.

Fig. 3.2

(a)

The child and sledge have a total mass of 70 kg . The component of the total weight of the child and sledge that acts down the slope is 80 N .

Determine

[ 4 ]

(i)

the frictional force on the sledge as it moves from B towards A,

frictional force =

[ 2 ]

$F=70 \times 0.50(=35)$

C1

frictional force =80-35
$=45 \mathrm{~N}$

A1

(ii)

the angle $\theta$ of the slope to the horizontal.

\theta=

[ 2 ]

$\sin \theta=80 /(70 \times 9.81)$

C1

$\theta=6.7^{\circ}$

A1

[Maximum number: 2]

A child's toy uses the spring in (a) to launch a ball of mass 0.020 kg vertically into the air. The ball is initially held against one end of the spring which has a compression of 0.045 m . The spring is then released to launch the ball. The kinetic energy of the ball as it leaves the toy is 0.72 J .

Determine the initial momentum of the ball as it leaves the toy.

momentum =

$E=\frac{1}{2} m v^{2}$

C1

p=m v

C1

$\begin{aligned} 0.72=1 / 2 \times 0.020 \times v^{2} \text { and } p=0.020 \times v p=0.17 \mathrm{Ns} \end{aligned}$

A1

All question bank results loaded

Covered syllabus points

3.1 Momentum and Newton’s laws of motion question 1

Question (a)

Question (b)

Question (i)

3.1 Momentum and Newton’s laws of motion question 2

Question (a)

Question (i)

Question (ii)

3.1 Momentum and Newton’s laws of motion question 3