(III) A 3.0-m-long steel chain is stretched out along the top level of a horizontal scaffold at a construction site, in such a way that 2.0 m of the chain remains on the top level and 1.0 m hangs vertically, Fig. 7–27. At this point, the force on the hanging segment is sufficient to pull the entire chain over the edge. Once the chain is moving, the kinetic friction is so small that it can be neglected. How much work is performed on the chain by the force of gravity as the chain falls from the point where 2.0 m remains on the scaffold to the point where the entire chain has left the scaffold? (Assume that the chain has a linear weight density of 24 N/m.) <IMAGE>

(II) A constant force F→ = (2.0 î + 4.0 ĵ) N acts on an object as it moves along a straight-line path. If the object’s displacement is d→ = (1.0 î + 5.0 ĵ) m, calculate the work done by using these alternate ways of writing the dot product:

(a) W = Fd cosθ ; (b) W = Fₓdₓ + Fᵧdᵧ .

(II) A child is pulling a wagon down the sidewalk. For 5.0 m the wagon stays on the sidewalk and the child pulls with a horizontal force of 22 N. Then one wheel of the wagon goes off onto the grass so the child has to pull with a horizontal force of 38 N at an angle of 12° to the side for the next 3.0 m. Finally the wagon gets back on the sidewalk so the child makes the rest of the trip, 8.5 m, with a force of 22 N. How much total work did the child do on the wagon?

An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mass was 82 kg and his terminal velocity was 45 m/s, estimate:

(c) the work done on him by air resistance as he fell. Model him as a particle.

(II) Consider a force F₁ = A /√x which acts on an object during its journey along the x axis from x = 0.0 to x = 1.0m, where A = 3.0 N • m¹⸍² . Show that during this journey, even though F₁ is infinite at x = 0.0, the work W done on the object by this force is finite, and determine W.

Two forces, F₁→ = (1.50î - 0.80 ĵ + 0.70k̂) N and F₂→ = ( - 0.70î + 1.20 ĵ) N, are applied on a moving object of mass 0.20 kg. The displacement vector of the object while the two forces act is d→ = (6.0 î + 8.0 ĵ + 5.0 k̂ ) m . What is the work done by the two forces?

You pull a 5kg box vertically up with a constant 100N force for 2m. How much work do you do?

You push a 3kg box against a wall for a distance of 2m with a force of 40N that makes a 53° angle with the horizontal, as shown. Calculate the work done by gravity.