


1. 

The system below is in equilibrium. 








Frictional forces can be neglected. 

a) 
Given that m_{2}=0.2kg,
calculate m_{1}. 

b) 
Calculate the gravitational potential energy gained by m_{1}
if m_{2} is pushed down 0.3m. 

c) 
If m_{1} is removed and replaced by an object of mass 2m_{1},
calculate the acceleration of the system. 

d) 
Calculate the total kinetic energy of the system after 2s of
acceleration (with the mass 2m_{1} in place and assuming
that v_{o}=0). 



2. 

A body rests, without slipping, on a plane which is inclined at
30° to the horizontal. 

a) 
Draw a diagram showing the forces acting on the body. 

b) 
If the body has a mass of 2kg,
calculate the magnitude of the force of friction acting on it. 



3. 

An object of mass m=5kg is
being pulled up an inclined plane which is at 40° to the
horizontal. 


The object is pulled at a constant speed of 0.8ms^{1}
by a force which acts parallel to the inclined plane. 


The coefficient of friction between the object and the plane is
0.2 

a) 
Draw a diagram showing the forces acting on the object. 

b) 
Calculate the magnitude of the force of friction acting on the
object. 

c) 
Calculate the gain in gravitational potential energy when the
object has moved 0.5m (measured
parallel to the slope). 

d) 
Calculate the total work done in pulling
the block 0.5m (measured along the
slope). 



4. 

A piece of metal is given an initial
kinetic energy, K, near the bottom of a plane inclined at
θ degrees to the horizontal. 


The coefficient of dynamic friction between
the metal and the inclined plane is μ. 











The centre of gravity of the piece of metal
moves through a vertical distance, h, before coming to rest. 


Using the principle of conservation of
energy, show that the relation between h and K is 


