Work done by gravity help!?

Question

A 4.5 kg block slides down a frictionless incline
making an angle of 31degrees with the horizontal.
The acceleration of gravity is 9.81 m/s^2
a) Find the work done by the gravitational
force when the block slides 4.1 m (measured
along the incline). Answer in units of J

b) What is the total work done on the block?
Answer in units of J.

c) What is the speed of the block after it has moved 4:1 m if it starts from rest? Answer in
units of m/s.

d) What is its speed after 4.1 m if it starts
with an initial speed of 1.4 m/s? Answer in
units of m/s.

I know it seems like a lot - I'm not asking for answers, just a little guidance on what equations to use - I'm sure i can figureit out then... Thanks so much!

Answer 1

a) Figure out how much potential energy it lost. That's the amount of work gravity did. Gravity is the reason for potential energy.

b) Hmmm, trick question? What else would be doing any work? Same amount of Joules from a.

c)That loss of potential energy has become kinetic energy. You can get it's velocity downslope from
PE = KE = (1/2)m*v^2

d) In this case, the block started with a combination of PE and KE. After sliding on a frictionless slide, the total energy is still the same. The same amount of energy as befpre will have converted from PE to KE.