Questions
— CAIE
M1
(732 questions)
CAIE
M1
2007
November
Q5
- The normal and frictional components of the contact force exerted on the ring by the rod are \(R \mathrm {~N}\) and \(F\) N respectively. Find \(R\) and \(F\) in terms of \(T\).
- The coefficient of friction between the rod and the ring is 0.7 . Find the value of \(T\) for which the ring is about to slip.
- A man walks in a straight line from \(A\) to \(B\) with constant acceleration \(0.004 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). His speed at \(A\) is \(1.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and his speed at \(B\) is \(2.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the time taken for the man to walk from \(A\) to \(B\), and find the distance \(A B\).
- A woman cyclist leaves \(A\) at the same instant as the man. She starts from rest and travels in a straight line to \(B\), reaching \(B\) at the same instant as the man. At time \(t \mathrm {~s}\) after leaving \(A\) the cyclist's speed is \(k \left( 200 t - t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(k\) is a constant. Find
(a) the value of \(k\),
(b) the cyclist's speed at \(B\). - Sketch, using the same axes, the velocity-time graphs for the man's motion and the woman's motion from \(A\) to \(B\).
CAIE
M1
2011
November
Q5
- Show that \(\mu \geqslant \frac { 6 } { 17 }\).
When the applied force acts upwards as in Fig. 2 the block slides along the floor.
- Find another inequality for \(\mu\).
CAIE
M1
2012
November
Q5
- Find the value of \(\theta\).
At time 4.8 s after leaving \(A\), the particle comes to rest at \(C\).
- Find the coefficient of friction between \(P\) and the rough part of the plane.
CAIE
M1
2014
November
Q6
- the work done against the frictional force acting on \(B\),
- the loss of potential energy of the system,
- the gain in kinetic energy of the system.
At the instant when \(B\) has moved 0.9 m the string breaks. \(A\) is at a height of 0.54 m above a horizontal floor at this instant.
(ii) Find the speed with which \(A\) reaches the floor.
\(6 \quad A B C\) is a line of greatest slope of a plane inclined at angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.28\) and \(\cos \alpha = 0.96\). The point \(A\) is at the top of the plane, the point \(C\) is at the bottom of the plane and the length of \(A C\) is 5 m . The part of the plane above the level of \(B\) is smooth and the part below the level of \(B\) is rough. A particle \(P\) is released from rest at \(A\) and reaches \(C\) with a speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The coefficient of friction between \(P\) and the part of the plane below \(B\) is 0.5 . Find
(i) the acceleration of \(P\) while moving - from \(A\) to \(B\),
- from \(B\) to \(C\),
(ii) the distance \(A B\),
(iii) the time taken for \(P\) to move from \(A\) to \(C\).
CAIE
M1
2017
November
Q6
- Show that the coefficient of friction between \(P\) and the plane is \(\frac { 4 } { 3 }\).
A force of magnitude 10 N is applied to \(P\), acting up a line of greatest slope of the plane, and \(P\) accelerates at \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). - Find the value of \(m\).
CAIE
M1
2019
November
Q4
- Find the acceleration of the blocks and the tension in the string.
- At a particular instant, the speed of the blocks is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the time, after this instant, that it takes for the blocks to travel 0.65 m .
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A small ring \(P\) is threaded on a fixed smooth horizontal \(\operatorname { rod } A B\). Three horizontal forces of magnitudes \(4.5 \mathrm {~N} , 7.5 \mathrm {~N}\) and \(F \mathrm {~N}\) act on \(P\) (see diagram). - Given that these three forces are in equilibrium, find the values of \(F\) and \(\theta\).
- It is given instead that the values of \(F\) and \(\theta\) are 9.5 and 30 respectively, and the acceleration of the ring is \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Find the mass of the ring.
CAIE
M1
Specimen
Q4
- Find the values of \(F\) and \(R\).
- Initially the bead is at rest at \(A\). It reaches \(B\) with a speed of \(11.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the mass of the bead.