MTH5P2B: Connected particles

Pulleys

Problems involve two weights either side of a pulley. The heavier weight pulls on the lighter causing both to accelerate in one direction with a common acceleration.

calculation of acceleration ‘a’

calculation of tension ‘T’

Example

A 3 kg mass and a 5 kg mass are connected over a pulley by a light inextensible string.
When the masses are released from rest, what is:
i) the acceleration of each mass?
ii) the tension in the string
(Take g=9.8 ms^-2 . Answer to 2 d.p.)

i)

ii)

Towe-bar/towe-rope/chains

Usually one body pulled horizontally by another with each linked by a towe-bar or similar. This is similar to the pulley but drawn out in a line.

assuming no friction,

calculation of acceleration ‘a’

calculation of tension ‘T’

Example

A car of mass 600 kg towes a trailer of mass 250 kg in a straight line using a rigid towe-bar.
The resistive force on the car is 200N.
The resistive force on the trailer is 80N.
If the forward thrust produced by the engine of the car is 800 N, what is(to 3 d.p.)
i) the acceleration of the car
ii) the tension in the towe-bar

i) looking at all the forces on the car and trailer together

ii)

Inclined plane with pulley

The pulley at the end just changes the direction of the force. problems involve the resolved component of the weight of the object down the plane.

for a mass sliding down a smooth incline

for a mass pulled up an incline via a pulley

Example

A 2 kg mass on a smooth 30^o plane is connected to a 5 kg mass by a light inextensible string passing over a pulley at the top of the plane.
When the particles are released from rest the 2 kg mass moves up the plane.
i) what is the acceleration of the 2 kg & 5 kg masses?
ii) What is the tension in the string?

i)

ii)

Mass ascending or descending in a lift

it is important to remember that there are only two forces on the body in the lift – the weight down and the reaction of the floor up.

Example

A person of mass 100 kg stands in a lift.
What is the force exerted by the lift floor on the person when the lift is:
i) moving upwards at 3 ms^-1
ii) moving downwards at 4 ms^-1

i)

ii)