Physics energy questions

Question

1.A person eats an 141,000 J snack before working out. If the person uses all of their eaten energy to lift a 14 kg weight. How high can they lift the weight?

2.A spring has 2,305 J of energy stored in it. It launches a block 21.4 m into the air (straight up). How much mass must the block have?

3.A person runs up 25 stairs of height 0.29 m. The person weighs 59 N. How much energy does it take for the person to reach the top of the stairs?

4.A block is push up a friction-less incline plane of length 8 m as seen below. The mass of the block is 25 kg and the angle of incline is 32 degrees. How much energy will in take to push the block up to the top of the incline?

*answer and explanation please*

Answer 1

1) Weight = mass x acceleration of gravity = 14 kg x 9.8 m/s² = 137.2 kg-m/s² = Force that must be lifted

Work = Energy = Force x Distance or 137.2 kg-m/s² x Distance = 141,000 kg-m²/s²

So, Distance = 141,000/137.2 = 1027.7 meters

2) Energy = Force x Distance or 2,305 kg-m²/s² = mass x g x 21.4 meters

So, mass x g = 2,305/21.4 = 107.7 Kg-m²/s²

But, mass = 107.7/9.8 = 11 kg

3) 25 stairs x .29 m = 7.25 meters total

59 N = 59 Kg-m/s²

Energy = Force x Distance = 59 Kg-m/s² x 7.25 m = 427.75 Kg-m²/s² = 427.75 Joules

4) The amount of work is the same as if the weight were lifted straight up at the end of the inclined plane. That height is 8sin(32) = 4.24 meters

So, Force x Distance = 25Kg x 9.8 m/s² x 4.24 meters = 1038.6 Kg-m²/s² = 1038.6 Joules