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Cambridge International AS and A Level

Name of student MIKE GREEN Date
Adm. number Year/grade 1998 Stream Mike Green
Subject Mechanics 1 (M1) Variant(s) P41, P42, P43
Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 6 4 6 5 7 5 33

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Question 1 Code: 9709/41/M/J/18/3, Topic: -


A particle $P$ of mass $8 \mathrm{~kg}$ is on a smooth plane inclined at an angle of $30^{\circ}$ to the horizontal. A force of magnitude $100 \mathrm{~N}$, making an angle of $\theta^{\circ}$ with a line of greatest slope and lying in the vertical plane containing the line of greatest slope, acts on $P$ (see diagram).

$\text{(i)}$ Given that $P$ is in equilibrium, show that $\theta=66.4$, correct to 1 decimal place, and find the normal reaction between the plane and $P$. $[4]$

$\text{(ii)}$ Given instead that $\theta=30$, find the acceleration of $P$. $[2]$

Question 2 Code: 9709/42/M/J/18/3, Topic: -


The three coplanar forces shown in the diagram have magnitudes $3 \mathrm{~N}, 2 \mathrm{~N}$ and $P \mathrm{~N}$. Given that the three forces are in equilibrium, find the values of $\theta$ and $P$. $[3]$

Question 3 Code: 9709/43/M/J/18/3, Topic: -


Coplanar forces of magnitudes $8 \mathrm{~N}, 12 \mathrm{~N}$ and $18 \mathrm{~N}$ act at a point in the directions shown in the diagram. Find the magnitude and direction of the single additional force acting at the same point which will produce equilibrium. $[6]$

Question 4 Code: 9709/41/O/N/18/3, Topic: -

A van of mass $2500 \mathrm{~kg}$ descends a hill of length $0.4 \mathrm{~km}$ inclined at $4^{\circ}$ to the horizontal. There is a constant resistance to motion of $600 \mathrm{~N}$ and the speed of the van increases from $20 \mathrm{~m} \mathrm{~s}^{-1}$ to $30 \mathrm{~m} \mathrm{~s}^{-1}$ as it descends the hill. Find the work done by the van's engine as it descends the hill. $[5]$

Question 5 Code: 9709/42/O/N/18/3, Topic: -


The velocity of a particle moving in a straight line is $v \mathrm{~m} \mathrm{~s}^{-1}$ at time $t$ seconds. The diagram shows a velocity-time graph which models the motion of the particle from $t=0$ to $t=T$. The graph consists of four straight line segments. The particle reaches its maximum velocity $V \mathrm{~m} \mathrm{~s}^{-1}$ at $t=10$.

$\text{(i)}$ Find the acceleration of the particle during the first 2 seconds.

$\text{(ii)}$ Find the value of $V$. $[2]$

At $t=6$, the particle is instantaneously at rest at the point $A$. At $t=T$, the particle comes to rest at the point $B.$ At $t=0$ the particle starts from rest at a point one third of the way from $A$ to $B$.

$\text{(iii)}$ Find the distance $A B$ and hence find the value of $T$. $[4]$

Question 6 Code: 9709/43/O/N/18/3, Topic: -

A particle of mass $1.2 \mathrm{~kg}$ moves in a straight line $A B$. It is projected with speed $7.5 \mathrm{~m} \mathrm{~s}^{-1}$ from $A$ towards $B$ and experiences a resistance force. The work done against this resistance force in moving from $A$ to $B$ is $25 \mathrm{~J}$.

$\text{(i)}$ Given that $A B$ is horizontal, find the speed of the particle at $B$. $[2]$

$\text{(ii)}$ It is given instead that $A B$ is inclined at $30^{\circ}$ below the horizontal and that the speed of the particle at $B$ is $9 \mathrm{~ms}^{-1}$. The work done against the resistance force remains the same. Find the distance $A B$. $[3]$

Worked solutions: P1, P3 & P6 (S1)

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