• A Level Maths

Demo

• A Level
• 1D Connected Particles

1. A man has a mass of 82 kg and is standing in a lift. The lift is moving upwards and decelerating at 0.5 m s^-2. Find the normal contact force exerted by the lift on the man.

762.6 N

2. A van of mass 5200 kg pulls a trailer of mass 1200 kg on a horizontal road. The driving force of the van's engine is 4800 N. Horizontal resisting forces of 600 N and 200 N act on the van and the trailer respectively. Find the tension in the coupling between the van and the trailer.

950 N

3. A crate of mass 120 kg is pulled vertically upwards by a cable. A box of mass 30 kg is attached to the underside of the crate by a light inextensible rope. The crate and box are accelerating upwards at 0.1 m s^-2. Find the tension in the rope.

297 N

4. A car of mass 1500 kg pulls a trailer of mass 500 kg on a straight horizontal road. Resistances to motion are constant at 200 N on the car and 100 N on the trailer. During the journey, a braking force is applied to the car, with the result that the car and trailer decelerate at a constant rate of 0.2 m s^-2. Find the braking force applied to the car.

100 N

5. A car of mass 1600 kg pulls a trailer of mass 400 kg on a straight horizontal road. The driving force of the car's engine is 5000 N. Resistances to motion are constant at 400 N on the car and 100 N on the trailer.
The coupling becomes disconnected when the car and trailer are moving at 20 m s$^{-1}$. Find the time taken for the trailer to come to rest.

80 seconds

6. A man of mass 80 kg is standing in a lift on a set of scales, holding a parcel of mass 3 kg by a piece of string. If the tension in the string is 23 N, what is the reading on the scales?

64.9 kg

7. A block, $A$, of mass 900 kg is connected to a smaller block, $B$, of mass 250 kg, via a light, rigid bar. The two blocks are resting on a rough horizontal surface. The coefficient of friction between $A$ and the surface of 0.1 and between $B$ and the surface of 0.2.
A force of 2000 N is applied to $A$ in a direction away from $B$. Calculate the acceleration of the system.

0.546 m s^-2

8. A block of mass 3 kg is held at rest on a horizontal table top. It is connected to a second block, of mass 2 kg, by means of a light, inextensible string which passes over a smooth pulley at the edge of the table. The 2 kg mass hangs freely. The system is released from rest, and the acceleration is observed as 1.4 m s^-2. Find, as a fraction, the coefficient of friction between the block and the table.

$\dfrac{3}{7}$

9. Two particles masses 3 kg and $m$ kg hang freely, attached to the ends of a light inextensible string which passes over a smooth pulley.
When the system is released from rest, the acceleration of the system is 1.96 m s^-2. Find the largest possible value of $m$.

4.5 kg

10. The diagram below shows three particles connected via light inextensible strings, which pass over smooth pegs. Given that particle $A$ has a mass of 3 kg, particle $B$ has a mass of 5 kg, and particle $C$ has a mass of 4 kg, and that the table $C$ sits on is smooth, find, in terms of $g$, the acceleration of the system.

$\dfrac{1}{6}g$

11. Two particles $A$ and $B$ have mass 0.4 kg and 0.3 kg respectively. The particles are attached to the ends of a light inextensible string and hang freely. The string passes over a smooth pulley and both particles are initially 1 m above the floor.
The particles are released from rest. The string breaks after 0.5 s. Find the additional time taken for $B$ to hit the floor.

0.566

12. Two particles $A$ and $B$ have masses $5m$ and $km$ respectively, where $k < 5$. The particles are connected by a light inextensible string which passes over a smooth light fixed pulley and hang freely. Initially, $A$ and $B$ are at the same height above a horizontal plane.
After releasing the system from rest, $A$ descends with acceleration $0.25g$. After $1.2$ s, $A$ reaches the plane and does not bounce. Find the greatest height reached by $B$ above the plane.

2.205 m

13. Louise does not want to eat her fruits and plays with them instead. She attaches an apple of mass 0.1 kg to one end of a string, passes the string over a pulley, and attaches the other end of the string to a banana, of mass 0.05 kg. Louise holds the apple and banana level, and instantaneously releases both of them. In the subsequent motion, neither fruit reaches the pulley or lands on the ground.
Louise gets bored after 1 second and cuts the string. Find the time it takes for the banana to return to its initial height.

1 second

14. Two particles are connected by a light inextensible string which passes over a smooth pulley and are hanging freely. Initially, they are 3.15 m above horizontal ground. The particles are released from rest. After 1.5 seconds, one particle hits the ground and does not rebound.
Find the exact time taken for the the string to become taut again.

$\dfrac{6}{7}$ seconds

15. Two particles $A$ and $B$ have masses 2 kg and 10 kg, respectively. The two particles are connected by a light inextensible string which passes over a pulley and both hang freely 3 m above the ground.
Find the maximum height above the ground that $A$ reaches after the particles are released from rest.

5 m

16. A particle $A$ of mass 5 kg is connected to a small box $B$ of mass 7.5 kg by a light inextensible string. The string passes over a light smooth pulley $P$, which is located at the end of a rough horizontal house roof. $B$ is held on the roof with $A$ hanging vertically off the end of the roof, and the coefficient of friction between $B$ and the roof is $0.2$.
Upon releasing the system from rest, $A$ travels 2.8 m before the string breaks. Calculate the total distance travelled by $B$ before it comes to a stop.

6.72 m

17. The diagram below shows three particles connected via light inextensible strings, which pass over smooth pegs. Given that particle $A$ has a mass of 3 kg, particle $B$ has a mass of 8 kg, and particle $C$ has a mass of 5 kg, and that the coefficient of friction between $C$ and the table is 0.7, find, in terms of $g$, the acceleration of the system.

$\dfrac{3}{32}g$

18. A block of mass 5 kg is held on a rough horizontal table. The block is connected to a light, inextensible string, which passes over a smooth pulley and is attached to a particle of mass $m$ kg, which hangs off the end of the table vertically below the pulley. The distance between the block and the pulley is 1 m, and the coefficient of friction between the block and the table is 0.3. The block is released and, after 1 s, the string breaks before the particle hits the ground.
Find the values of $m$ such that the block will hit the pulley.

$m \geqslant 2.13$