As in Problem A above, a block of mass M starts from rest and is pushed up a frictionless ramp inclined at an angle θ above the horizontal by a constant force F. Use the work-energy theorem to find the block’s speed after it has been pushed a distance L up the incline. Your answer should be written in terms of M, θ, F, L and the acceleration due to gravity, g.

A(i)

The solution to this question is shown on the second uploaded image

A(ii)

The final speed is

B

The block speed after a distance L  is  

Explanation:

From the question  

The net force i the x-direction is mathematically represented as

From the the diagram in the second uploaded image we see that

Therefore

Making a the subject

Applying the law of motion

where  u = 0 m/s and s =L

=>  

According to Energy conservation law and work theorem

           Workdone by F + Workdone by gravity = change in kinetic energy

Mathematically this is given as

   Since u = 0 m/s

the one with the highest speed

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