What is the power done by gravity to make a ball of mass 0.6 kg roll from 8.9 m above the ground to the bottom along a curved path if it takes 5.45 s to do so?

Consider a box, of mass 5 kg, being pushed along a horizonal surface a distance of 2.9 m in 16.2 seconds. The applied force is 165.7 N and is directed at an angle 0.7 radians as shown in the diagram below. What is the power exerted while moving the object?

Consider a hoop of mass 3.1 kg and radius 0.52 m that rolls without slipping down an incline. The hoop starts at rest from a height h = 2.7 m above the bottom of the incline and then rolls to the bottom.

(a) How much gravitational potential energy (relative to the ground on which it is built) is stored in an Egyptian pyramid, given its mass is about 6 ✕ 109 kg and its center of mass is 30.0 m above the surrounding ground?  J(b) What is the ratio of this energy to the daily food intake of a person (1.2 ✕ 107 J)?

With what initial speed must an object be projected vertically upward from the surface of Earth to rise to a maximum height equal to Earth’s radius? (Neglect air resistance.) Apply energy conservation.

You overindulged on a delicious dessert, so you plan to work off the extra calories at the gym. To accomplish this, you decide to do a series of arm raises holding a 5.5 kg weight in one hand. The distance from your elbow to the weight is 38 cm, and in each arm raise you start with your arm horizontal and pivot it until it is vertical. Assume that the weight of your arm is small enough compared with the weight you are lifting that you can ignore it. As is typical, your muscles are 20 % in converting the food energy they use up into mechanical energy, with the rest going into heat. If your dessert contained 350 food calories, how many arm raises must you do to work off these calories?

I feel like the hoop would reach the bottom faster because less energy is required to move it. is this correct? thank you!