Question1

A block of mass m1 = 4 kg moves from rest under the influence of a varying force F(x) = 4x + 38, where F is in Newtons and x is in meters, on a rough horizontal surface having a coefficient of kinetic friction of 0.2. The block is connected by a light cord passing over a small frictionless pulley to a second hanging block of mass m2 = 3 kg. If a system moves from x= 0 to x= 2m, calculate:
1) work done by the force F(x) to move m1 from x= 0 to x= 2m.

2) Change in the potential energy of each mass

3) work done by friction.

4) The change in the kinetic energy of the system.

Question2

A non-uniform, 2.0 m long ladder weighing 400 N leans against a smooth vertical wall (no friction). The ladder makes an angle of 30 degrees with vertical. The coefficient of static friction at ground is 0.3. A child with weight of 300 N can climb the ladder of 1.2 m before it starts to slide down. The location of the centre of gravity of the ladder relative to ground is? The normal force coming from a smooth wall is?