Question

1. Given the table below, about how much force does the rocket engine exert on the 5.0 kg payload?

Distance traveled with rocket engine firing (m)	Payload final velocity (m/s)
500	250
490	250
1020	360
505	254

2.Look at the figure below.

You compress a spring by x, and then release it. Next you compress the spring by 3x. How much more work did you do the second time than the first?

3. A crane is lifting construction materials from the ground to an elevation of 85 m. Over the first 10 m, the motor linearly increases the force it exerts from 0 to 30 kN. It exerts that constant force for the next 65 m, and then winds down to 0 N again over the last 10 m, as shown in the figure.

What is the total work done on the construction materials?

4. A model drag car is being accelerated along its track from rest by a motor with a force of 87 N, but there is a drag force of 35 N due to the track. What is the kinetic energy after 5 m of travel?

5. You are launching a 2 kg potato out of a potato cannon. The cannon is 1.8 m long and is aimed 25 degrees above the horizontal. It exerts a 52 N force on the potato. What is the kinetic energy (in J) of the potato as it leaves the muzzle of the potato cannon?

Answer 1

given

m = 5 kg

Distance traveled with rocket engine firing (m) = d	Payload final velocity (m/s) = v
500	250
490	250
1020	360
505	254

F₁ = 0.5 m v² / d

= 0.5 x 5 x 250² / 500

F₁ = 312.5 N

F₂ = 0.5 m v² / d

= 0.5 x 5 x 250² / 490

F₂ = 318.87 N

F₃ = 0.5 m v² / d

= 0.5 x 5 x 360² / 1020

F₃ = 317.64 N

F₄ = 0.5 m v² / d

= 0.5 x 5 x 254² / 505

F₄ = 319.386 N

F = ( F₁ + F₂ + F₃ + F₄ ) / 4

= ( 312.5 + 318.87 + 317.64 + 319.386 ) / 4

F = 317 N nearly