9. Work & Energy

Consider a force F(𝓍) = A𝓍^3/2 acting on an object moving in a straight line. Assume that A = 10.0 N/m^z. Calculate the work done by this force as the object moves from 𝓍 = 0 to 𝓍 = 3.0 m.

The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.65 m. What is the maximum amount of work it could do on the nail? Why do people not just “let it fall” but add their own force to the hammer as it falls?

A 2800-kg space vehicle, initially at rest, falls vertically from a height of 2900 km above the Earth’s surface. Determine how much work is done by the force of gravity in bringing the vehicle to the Earth’s surface.

Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a horizontal force of about 15 N.

A 55.0-kg firefighter climbs a flight of stairs 28.0 m high at constant speed. How much work does she do?

Two forces, ${\vec{F}}_1=(1.50\hat{i}-0.80\hat{j}+0.70\hat{k})\text{ N}$ and ${\vec{F}}_2=(-0.70\hat{i}+1.20\hat{j})\text{ N}$, are applied on a moving object of mass 0.20 kg. The displacement vector of the object while the two forces act is $\overrightarrow{d}=(6.0\hat{i}-8.0\hat{j}+5.0\hat{k})\text{ m}$. What is the work done by the two forces?

How much work is done when a constant force of $60 N$ is used to pull a sled a distance of $5 m$ in the direction of the force?

A factory worker pushes a $30.0$-kg crate a distance of $4.5$ m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is $0.25$. What is the total work done on the crate?

In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.25 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?

(II) A lever such as that shown in Fig. 7–20 can be used to lift objects we might not otherwise be able to lift. Show that the ratio of output force, F_O, to input force, F_I, is related to the lengths ℓ_I and ℓ_O from the pivot by F_O / F_I = ℓ_I / ℓ_O. Ignore friction and the mass of the lever, and assume the work output equals the work input.

<Image>