Question

Hello everyone I would like your help on this exercise because the physics I have a little difficulty. Here is the statement:

A child launches a blue cart of mass m= 150 g in A of altitude zA= 0 on an inclined plane of an angle α = 30° with respect to the horizontal. The cart then climbs to point C where it stops before descending in reverse. This blue cart is not subject to any frictional force between A and C.
1°-What are the forces acting on the car during its journey from A to C ?
2°-What can we say about the mechanical energy of the car? Why?
3°-Determine the velocity vA with which the child launches the cart in Asknowing that the point C is at the altitude zC= 0,80 m

The child then launches a red cart of the same mass as the blue one with a speed of 4.0 m/s. This car reaches only a height of 0.55 m.
4°-Show that the mechanical energy for this red car is not conserved.
5°-Assuming that the frictional force exerted on this car during all its journey is constant, calculate the work of this force noted f.
6°-Determine then the value of f.

Data: Gravity field: g= 9,81 N/kg

Answer 1

Fn = m g cos 30 = .15 * 9.81 * .866 = 1.27 N force of plane on car

Fp = m g sin 30 = .15 * 9.81 * 1/2 = .736 N force along plane

m g h = W = potential energy of car = original mechanical energy

1/2 m v^2 = m g h equating PE and KE

v^2 = 2 g h = 2 * 9.81 * .8

v = 3.96 m/s original speed of blue cart

Launch energy of red cart

1/2 m v^2 = .15 / 2 * 16 = 1.2 J launch energy of red cart

m g h = .15 * 9.81 * .55 = .81 J potential energy of red cart

Wf = (1.2 -.81) J = .39 J work done against friction