Forces Connected Bodies

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

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

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

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

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

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

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

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

Got brain ache yet ? Unlucky

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?

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 = 6.25 + 20 = 26.25 N

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

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

(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