9. Work & Energy

The three ropes shown in the bird's-eye view of FIGURE EX9.18 are used to drag a crate 3.0 m across the floor. How much work is done by each of the three forces?

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?

Consider a force F₁ = $A/\sqrt{x}$ which acts on an object during its journey along the x axis from x = 0.0 to x = 1.0m, where A = 3.0 Nm¹⸍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.

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 magnitude of force must the worker apply?

A 1000 kg elevator accelerates upward at 1.0 m/s² for 10 m, starting from rest. How much work does the tension in the elevator cable do on the elevator?

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?

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of $1.80\times {10}^6$ N, one $14°$ west of north and the other $14°$ east of north, as they pull the tanker $0.75$ km toward the north. What is the total work they do on the supertanker?

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.)

A 25 kg air compressor is dragged up a rough incline from ${\vec{r}}_1=(1.3\hat{ı}+1.3\hat{ȷ})\text{m}$ to ${\vec{r}}_2=(8.3\hat{ı}+2.9\hat{ȷ})\text{m}$, to where the y-axis is vertical. How much work does gravity do on the compressor during this displacement?

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

The energy used to pump liquids and gases through pipes is a significant fraction of the total energy consumption in the United States. Consider a small volume V of a liquid that has density ρ. Assume that the fluid is nonviscous so that friction with the pipe walls can be neglected. An upward-pushing force from a pump lifts this volume of fluid a height h at constant speed. How much work does the pump 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.

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 $0.25$. How much work is done on the crate by this force?

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) $W=F_x{d}_x+F_y{d}_y$.