Pulleys

1
21-Nov-09
Pulleys
2
Two masses are attached to a light inextensible
string and this runs freely over a
pulley. Calculate a) The acceleration b) The
tension in the string c) The reaction on the
pulley
T
T
1kg
4kg
3
F ma g T a (1)
T - 4g 4a (2) (1) (2) -3g 5a
a -3g/5 a - 5.9 ms-2
T
T
1kg
4kg
4
Substitute a - 5.9 into (1) g T a 9.8
T -5.9 T 9.8 5.9 T 15.9
N Reaction on the pulley is 2T 31.8 N
T
T
1kg
4kg
5
Reaction on the pulley Using Newtons third law
to every action there is an equal and opposite
reaction 2T 31.8 N
T
T
1kg
4kg
6
T
? 0.2
1kg
D
mg cos300
T
300
mg sin300
4kg
A mass of 4 kg acting on an inextensible rope is
pulling a particle up a slope as shown. Calculate
a) the tension in the string b) acceleration of
the particle and c) reaction on the pulley
7
Coefficient of friction ? 0.2

• Resistance to motion is
• the friction force
• ?mgcos300
• ii) the force on the particle due to gravity
• mgsin300

1kg
D
mg cos300
300
D mgsin30 ?mgcos30 D 0.5g 0.173g D 6.6 N
mg sin300
8
T

D 6.6N
F ma 4g - T 4a (1) T 6.6
a (2) (1) (2) 4g 6.6 5a
5a 32.6 a 6.5 ms-2
T
4kg
9
T

D 6.6N
T
Substitute a 6.5 into (2) T 6.6 a (2)
T - 6.6 6.5 T 13.1 N
4kg
10
T

D 6.6N
Reaction on the pulley using Newtons third law
T
Using sine rule R/sin120 T/3in30 R
T(sin120)/sin30 R 22.68 N
R
T
1200
4kg
T