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?

Objects that rotate in air or water experience a torque due to drag. With quadratic drag, a drag torque that's negligible at low rpm quickly becomes significant as the rpm increases. Consider a square bar with cross section a x a and length L. It is rotating on an axle through its center at angular velocity ω in a fluid of density ρ. Assume that the drag coefficient C_𝒹 is constant along the length of the bar. Find an expression for the magnitude of the drag torque on the bar. Hint: Begin by considering the drag force on a small piece of the bar of length dr at distance r from the axle.

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.

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.

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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.

A package of mass m is placed onto a horizontal conveyor belt moving at speed v (Fig. 7–32). The coefficient of kinetic friction between package and belt is μ_k. How much of this work is done against friction and how much to accelerate the package?

A softball having a mass of 0.25 kg is pitched horizontally at 120 km/h. By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distance between the plate and the pitcher is about 15 m.

A constant force $\vec{F}=(2.0\hat{i}+4.0\hat{j})\text{ N}$ acts on an object as it moves along a straight-line path. If the object’s displacement is $\vec{d}=(1.0\hat{i}+5.0\hat{j})\text{ m}$, calculate the work done by using these alternate ways of writing the dot product:

(a) $W=Fd\cos \theta$; (b) $W=F_x{d}_x+F_y{d}_y$.