1. Forces
Connected Bodies

2. T T
m is the mass of the block
m2g
g is gravity (9.8 ms-2)
m1g
Do you recognise this ?

3. So if you resolve the forces when it’s in equilibrium you get ?A B C D
T = m1g
T = m2g
m1 = m2
All of the above

4. And then it starts to move
Resolve the forces and type in your solution for T T
m is the mass of the block
g is gravity (9.8 ms-2)
m2g
m1g
Don’t use the mass suffixes in your answers

5. And your answer should look something like this . . . . .
Masses of 3 kg and 5 kg are at the ends of a light string which passes over a smooth fixed peg. Calculate the accelerations of the bodies and the tension in the string.
And your answer should look something like this
Resolving forces and using F=ma
5kg mass 5g-T = 5a using a to find T
3kg mass T-3g = 3a T-3g = 3 x 2.5
Adding the equations gives T = 37.5 N
2g = 8a
a=2.5ms-2

6. What happens on a smooth table?R T
m1g
m2g
Click to find out
Motion
No motion
Ball T = m2g m2g-T = m2a
Block Horizontally T = m2g T=m2g
Vertically R = m1g R = m1g

7. F≤R What happens on a rough table? R T m1g m2g Click to find out
Motion
No motion
Ball T = m2g m2g-T = m2a
Block Horizontally T - F = m2g T – F =m2a
Vertically R = m1g R = m1g

8. T mgsina F≤R a And now for a block and ball in equilibrium mg
Resolve for the ball
Resolve for the block parallel to the plane

9. So what happens when the block starts to move?
mgsina
F≤R a mg
Resolve for the ball
Resolve for the block parallel to the plane

10. Got brain ache yet ?
Unlucky

11. And now with numbers ! R T m1g m2g
A 5 kg mass on a fixed rough table (= 0.4) is connected to a mass of
3 kg hanging freely by a string passing over a small, well-oiled pulley at
the edge of the table. What happens when the system is released?

12. 3 minutes later the answer appears
Resolving forces parallel to the plane
T - F = 5a
R = 5g
Resolving forces for the ball
3g – T = 3a
We also know
F=R F = 0.4R = 2g
So we have
3g – F = 8a 8a = g so a = 1.25ms-2
Giving
T – F = 5a T = 5a + F = = N

13. More questions
1 Masses of 3 kg and 5 kg are at the ends of a light string which passes over a smooth fixed peg. Calculate the accelerations of the bodies and the tension in the string.
Click here for answers pg 19
Click to advance slide

14. 2. A particle of mass m kg moves up a line of greatest slope of a rough plane inclined at 21◦ to the horizontal. The frictional and normal components of the contact force on the particle have magnitudes F N and R N respectively. The particle passes through the point P with speed 10ms−1, and 2 s later it reaches its highest point on the plane.
(i) Show that R = 9.336m and F = 1.416m, each correct to 4 significant figures [5]
(ii) Find the coefficient of friction between the particle and the plane [1]
After the particle reaches its highest point it starts to move down the plane.
(iii) Find the speed with which the particle returns to P. [5]
Nov 2006 P4
Click here for answers pg 19
Click to advance slide

15. (b) Find the tension in the string and say what will happen when
3 A block of mass 10 kg rests on a horizontal table, the coefficient of friction between block and table being 0.3. The block is attached to a hanging mass of M kg by a string which passes over a smoothly running pulley at the edge of the table.
(a) Draw diagrams to show the forces on (i) the block (ii) the hanging mass.
(b) Find the tension in the string and say what will happen when
(i) M=2
(ii) M=5.
Click here for answers pg 19
Click to advance slide