?An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a

Rank the following velocities according to the kinetic energy a particle will have with each velocity, greatest first: (a)\(\vec{v}=4 \hat{i}+3 \hat{j}\), (b) \(\vec{v}=-4 \hat{i}+3 \hat{j}\), ©\(\vec{v}=-3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}\), (d) \(\vec{v}=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}\) (e)\(\vec{v}=5 \hat{i}\), and (f) \(v=5 \mathrm{~m} / \mathrm{s} \text { at } 30^{\circ}\) to the horizontal. Text Transcription: Arrow right over v=4i +3j Arrow right over v= -4i +3j Arrow right over v= -3i +4j Arrow right over v= -3i -4j Arrow right over v= 5i v=5m/s at 30^circ

Figure 7-16a shows two horizontal forces that act on a block that is sliding to the right across a frictionless floor. Figure 7-16b shows three plots of the block’s kinetic energy K versus time t. Which of the plots best corresponds to the following three situations: (a)\(F_{1}=F_{2}, \text { (b) } F_{1}>F_{2} \text {, (c) } F_{1}<F_{2}\)? Text Transcription: f_1-f_2 f_1>f_2 f_1<f_2

Is positive or negative work done by a constant force \(\vec{F}\) on a particle during a straight-line displacement \(\vec{d}\) if (a) the angle between \(\vec{F}\) and \(\vec{d}\) is \(30^{\circ}\); (b) the angle is \(100^{\circ}\); (c) \(\vec{F}=2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}\) and \(\vec{d}=-4 \hat{i}\)? Text Transcription: arrow right over F arrow right over d 30^circ 100^circ arrow right over F=2i -3j arrow right over d= - 4i

In three situations, a briefly applied horizontal force changes the velocity of a hockey puck that slides over frictionless ice. The overhead views of Fig. 7-17 indicate, for each situation, the puck’s initial speed \(v_{i}\) , its final speed\(v_{f}\), and the directions of the corresponding velocity vectors. Rank the situations according to the work done on the puck by the applied force, most positive first and most negative last. Text Transcription: v_i v_f

The graphs in Fig. 7-18 give the x component \(F_{x}\) of a force acting on a particle moving along an x axis. Rank them according to the work done by the force on the particle from x = 0 to x = \(x\), from most positive work first to most negative work last. Text Transcription: F_x x_1

Figure 7-19 gives the x component \(F_{x}\) of a force that can act on a particle. If the particle begins at rest at x = 0, what is its coordinate when it has (a) its greatest kinetic energy, (b) its greatest speed, and (c) zero speed? (d) What is the particle’s direction of travel after it reaches x = 6 m? Text Transcription: F_x

In Fig. 7-20, a greased pig has a choice of three frictionless slides along which to slide to the ground. Rank the slides according to how much work the gravitational force does on the pig during the descent, greatest first.

Figure 7-21a shows four situations in which a horizontal force acts on the same block, which is initially at rest. The force magnitudes are \(F_{2}=F_{4}=2 F_{1}=2 F_{3}\). The horizontal component \(v_{x}\) of the block’s velocity is shown in Fig. 7-21b for the four situations. (a) Which plot in Fig. 7-21b best corresponds to which force in Fig. 7-21a? (b) Which plot in Fig. 7-21c (for kinetic energy K versus time t) best corresponds to which plot in Fig. 7-21b? Text Transcription: F_2=F_4=2F_1=2F_3 V_x

Spring A is stiffer than spring B (\(k_{A}>k_{B}\)). The spring force of which spring does more work if the springs are compressed (a) the same distance and (b) by the same applied force? Text Transcription: k_A > k_B

A glob of slime is launched or dropped from the edge of a cliff. Which of the graphs in Fig. 7-22 could possibly show how the kinetic energy of the glob changes during its flight?

In three situations, a single force acts on a moving particle. Here are the velocities (at that instant) and the forces: (1) \(\vec{v}=(-4 \hat{i})\) m/s,\(\vec{F}=(6 \hat{\mathrm{i}}-20 \hat{\mathrm{j}})\) N; (2)\(\vec{v}=(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})\) m/s,\(\vec{F}=(-2 \hat{\mathrm{j}}+7 \hat{\mathrm{k}})\) N; (3)\(\vec{v}=(-3 \hat{i}+\hat{j})\) m/s, F ? = \((2 \hat{i}+6 \hat{j})\) N. Rank the situations according to the rate at which energy is being transferred, greatest transfer to the particle ranked first, greatest transfer from the particle ranked last. Text Transcription: arrow right over v =(-4i) arrow right over F = (6i -20j) arrow right over v =(2i -3j) arrow right over F =(-2j +7k) arrow right over v = (- 3i +j) arrow right over F = (2i + 6j)

Figure 7-23 shows three arrangements of a block attached to identical springs that are in their relaxed state when the block is centered as shown. Rank the arrangements according to the magnitude of the net force on the block, largest first, when the block is displaced by distance d (a) to the right and (b) to the left. Rank the arrangements according to the work done on the block by the spring forces, greatest first, when the block is displaced by d (c) to the right and (d) to the left.

Figure 7-42 shows a cold package of hot dogs sliding rightward across a frictionless floor through a distance d = 20.0 cm while three forces act on the package. Two of them are horizontal and have the magnitudes \(F_{1}\)= 5.00 N and \(F_{2}\)= 1.00 N; the third is angled down by \(\theta=60.0^{\circ}\)and has the magnitude \(F_{1}\)= 4.00 N. (a) For the 20.0 cm displacement, what is the net work done on the package by the three applied forces, the gravitational force on the package, and the normal force on the package? (b) If the package has a mass of 2.0 kg and an initial kinetic energy of 0, what is its speed at the end of the displacement? Text Transcription: F_1 F_2 F_3 theta=60.0^circ

The only force acting on a 2.0 kg body as the body moves along an x axis varies as shown in Fig. 7-43. The scale of the figure’s vertical axis is set by \(F_s=4.0\mathrm{\ N}\). The velocity of the body at x = 0 is 4.0 m/s. (a) What is the kinetic energy of the body at x = 3.0 m? (b) At what value of x will the body have a kinetic energy of 8.0 J? (c) What is the maximum kinetic energy of the body between x = 0 and x = 5.0 m? Text Transcription: F_s = 4.0 N

A horse pulls a cart with a force of 40 lb at an angle of \(30^{\circ}\)above the horizontal and moves along at a speed of 6.0 mi/h. (a) How much work does the force do in 10 min? (b) What is the average power (in horsepower) of the force? Text Transcription: 30^circ

A 230 kg crate hangs from the end of a rope of length L = 12.0 m. You push horizontally on the crate with a varying force \(\vec{F}\) to move it distance d = 4.00 m to the side (Fig. 7-44). (a) What is the magnitude of \(\vec{F}\) when the crate is in this final position? During the crate’s displacement, what are (b) the total work done on it, (c) the work done by the gravitational force on the crate, and (d) the work done by the pull on the crate from the rope? (e) Knowing that the crate is motionless before and after its displacement, use the answers to (b), (c), and (d) to find the work your force \(\vec{F}\) does on the crate. (f) Why is the work of your force not equal to the product of the horizontal displacement and the answer to (a)? Text Transcription: arrow right over F

To pull a 50 kg crate across a horizontal frictionless floor, a worker applies a force of 210 N, directed \(20^{\circ}\) above the horizontal. As the crate moves 3.0 m, what work is done on the crate by (a) the worker’s force, (b) the gravitational force, and (c) the normal force? (d) What is the total work? Text Transcription: 20^circ

A force \(\vec{F}_{a}\) is applied to a bead as the bead is moved along a straight wire through displacement +5.0 cm. The magnitude of \(\vec{F}_{a}\) is set at a certain value, but the angle \(\phi\) between \(\ve\(\vec{F}_{a}\) on the bead for a range of \(\phi\)values; \(W_{0}\)= 25 J. How much work is done by \(\vec{F}_{a}\)if \(\phi\)is (a) \(64^{\circ}\) and (b)\(147^{\circ}\)? Text Transcription: Arrow right over F Pi w_0 64^circ 147^circ

How much work is done by a force\(\vec{F}=(2 x \mathrm{~N}) \hat{i}+(3 \mathrm{~N}) \mathrm{j}^{2}\), with x in meters, that moves a particle from a position \(\vec{r}_{i}\) = \((2 \mathrm{~m}) \hat{\mathrm{i}}+(3 \mathrm{~m}) \hat{\mathrm{j}}\) to a position \(\vec{r}_{f}=-(4 \mathrm{~m}) \hat{i}-(3 \mathrm{~m}) \hat{j}\)? Text Transcription: Arrow right over F = (2x N)iˆ + (3 N)j Arrow right over r_f = (2 m)i + (3 m)j Arrow right over r_f = ?(4 m)i ? (3 m)j

A 250 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 2.5 N/cm (Fig. 7-46). The block becomes attached to the spring and compresses the spring 12 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring? (Assume that friction is negligible.) (d) If the speed at impact is doubled, what is the maximum compression of the spring?

To push a 25.0 kg crate up a frictionless incline, angled at \(25.0^{\circ}\) to the horizontal, a worker exerts a force of 209 N parallel to the incline. As the crate slides 1.50 m, how much work is done on the crate by (a) the worker’s applied force, (b) the gravitational force on the crate, and (c) the normal force exerted by the incline on the crate? (d) What is the total work done on the crate? Text Transcription: 25.0^circ

Boxes are transported from one location to another in a warehouse by means of a conveyor belt that moves with a constant speed of 0.50 m/s. At a certain location the conveyor belt moves for 2.0 m up an incline that makes an angle of \(10^{\circ}\) with the horizontal, then for 2.0 m horizontally, and finally for 2.0 m down an incline that makes an angle of \(10^{\circ}\) with the horizontal. Assume that a 2.0 kg box rides on the belt without slipping. At what rate is the force of the conveyor belt doing work on the box as the box moves (a) up the \(10^{\circ}\) incline, (b) horizontally, and (c) down the \(10^{\circ}\) incline? Text Transcription: 10^circ

In Fig. 7-47, a cord runs around two massless, frictionless pulleys. A canister with mass m = 20 kg hangs from one pulley, and you exert a force \(\vec{F}\) on the free end of the cord. (a) What must be the magnitude of \(\vec{F}\)if you are to lift the canister at a constant speed? (b) To lift the canister by 2.0 cm, how far must you pull the free end of the cord? During that lift, what is the work done on the canister by (c) your force (via the cord) and (d) the gravitational force? (Hint: When a cord loops around a pulley as shown, it pulls on the pulley with a net force that is twice the tension in the cord.) Text Transcription: arrow right over F

A spring with a pointer attached is hanging next to a scale marked in millimeters. Three different packages are hung from the spring, in turn, as shown in Fig. 7-48. (a) Which mark on the scale will the pointer indicate when no package is hung from the spring? (b) What is the weight W of the third package?

An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a constant force of 200 N, toward the east, on the boat. Due to the angle of the sail, the wind causes the boat to slide in a straight line for a distance of 8.0 m in a direction \(20^{\circ}\) north of east. What is the kinetic energy of the iceboat at the end of that 8.0 m? Text Transcription: 20^circ

A force \(\vec{F}=(4.0 \mathrm{~N}) \hat{1}+c \hat{\jmath}\) acts on a particle as the particle goes through displacement\(\vec{d}=(3.0 \mathrm{~m}) \hat{i}-(2.0 \mathrm{~m}) \hat{j}\). (Other forces also act on the particle.) What is c if the work done on the particle by force \(\vec{F}\)is (a) 0, (b) 17 J, and (c) ?18 J? Text Transcription: arrow right over F =(4.0 N)i + cj arrow right over d = (3.0 m)i ? (2.0 m)j

A constant force of magnitude 10 N makes an angle of \(150^{\circ}\)(measured counterclockwise) with the positive x direction as it acts on a 2.0 kg object moving in an xy plane. How much work is done on the object by the force as the object moves from the origin to the point having position vector ( \((2.0 \mathrm{~m}) \hat{\mathrm{i}}-(4.0 \mathrm{~m}) \hat{\mathrm{j}}\)ˆ? Text Transcription: 150^circ (2.0m)i - (4.0m) j

In Fig. 7-49a, a 2.0 N force is applied to a 4.0 kg block at a downward angle \(\theta\)as the block moves rightward through 1.0 m across a frictionless floor. Find an expression for the speed \(v_{f}\)of the block at the end of that distance if the block’s initial velocity is (a) 0 and (b) 1.0 m/s to the right. (c) The situation in Fig. 7-49b is similar in that the block is initially moving at 1.0 m/s to the right, but now the 2.0 N force is directed downward to the left. Find an expression for the speed \(v_{f}\)of the block at the e\(\theta\) for \(\theta=0^{\circ}\) to \(\theta=0^{\circ}\). Interpret the graphs. Text Transcription: theta v_f theta=0^circ theta=90^circ

A force \(\vec{F}\)in the positive direction of an x axis acts on an object moving along the axis. If the magnitude of the force is F = \(10 e^{-x / 20}\)N, with x in meters, find the work done by \(\vec{F}\)as the object moves from x = 0 to x = 2.0 m by (a) plotting F(x) and estimating the area under the curve and (b) integrating to find the work analytically. Text Transcription: Arrow right over F 10e?x/2.0

A particle moves along a straight path through displacement \(\vec{d}=(8 \mathrm{~m}) \hat{\mathrm{i}}+c \hat{\mathrm{j}}\) while force \(\vec{F}=(2 \mathrm{~N}) \mathrm{i}-(4 \mathrm{~N}) \mathrm{j}\) acts on it. (Other forces also act on the particle.) What is the value of c if the work done by \(\vec{F}\) on the particle is (a) zero, (b) positive, and (c) negative? Text Transcription: arrow right over d = (8 m)i + cj arrow right over F = (2 N)i ? (4 N)j arrow right over F

As a particle moves along an x axis, a force in the positive direction of the axis acts on it. Figure 7-50 shows the magnitude F of the force versus position x of the particle. The curve is given by F = \(a / x^{2}\), with a = 9.0 N? \(\mathrm{m}^{2}\). Find the work done on the particle by the force as the particle moves from x = 1.0 m to x = 3.0 m by (a) estimating the work from the graph and (b) integrating the force function Text Transcription: a/x^2 m^2

A CD case slides along a floor in the positive direction of an x axis while an applied force \(\vec{F}_{\mathrm{a}}\) acts on the case. The forceis directed along the x axis and has the x component \(F_{a x}=9 x-3 x^{2}\), with x in meters and \(F_{a x}\) in newtons. The case starts at rest at the position x = 0, and it moves until it is again at rest. (a) Plot the work \(\vec{F}_{a}\)does on the case as a function of x. (b) At what position is the work maximum, and (c) what is that maximum value? (d) At what position has the work decreased to zero? (e) At what position is the case again at rest? Text Transcription: arrow right over F_a f_ax=9x-3x^2 arrow right over F_ax

A 2.0 kg lunchbox is sent sliding over a frictionless surface, in the positive direction of an x axis along the surface. Beginning at time t = 0, a steady wind pushes on the lunchbox in the negative direction of the x axis. Figure 7-51 shows the position x of the lunchbox as a function of time t as the wind pushes on the lunchbox. From the graph, estimate the kinetic energy of the lunchbox at (a) t = 1.0 s and (b) t = 5.0 s. (c) How much work does the force from the wind do on the lunchbox from t = 1.0 s to t = 5.0 s?

Numerical integration. A breadbox is made to move along an x axis from x = 0.15 m to x = 1.20 m by a force with a magnitude given by F = exp(?\(-2 x^{2}\) ), with x in meters and F in newtons. (Here exp is the exponential function.) How much work is done on the breadbox by the force? Text Transcription: -2x^2

In the block–spring arrangement of Fig. 7-10, the block’s mass is 4.00 kg and the spring constant is 500 N/m. The block is released from position \(x_{i}\)= 0.300 m. What are (a) the block’s speed at x = 0, (b) the work done by the spring when the block reaches x = 0, (c) the instantaneous power due to the spring at the release point \(x_{i}\), (d) the instantaneous power at x = 0, and (e) the block’s position when the power is maximum? Text Transcription: x_1

A force\(\vec{F}=(2.00 \hat{\mathrm{i}}+9.00 \mathrm{j}+5.30 \mathrm{k})\) N acts on a 2.90 kg object that moves in time interval 2.10 s from an initial position \(\vec{r}_{1}=(2.70 \hat{i}-2.90 \mathrm{j}+5.50 \hat{k})\) m to a final position \(\vec{r}_{2}\) = \((-4.10 \hat{i}+3.30 \hat{j}+5.40 \hat{k})\)m. Find (a) the work done on the object by the force in that time interval, (b) the average power due to the force during that time interval, and (c) the angle between vectors \(\vec{r}_{1}\)and\(\vec{r}_{2}). Text Transcription: arrow right over F = (2.00i + 9.00j + 5.30k) arrow right over r_1 = (2.70iˆ ? 2.90jˆ + 5.50k arrow right over r_2 4.10i + 3.30j + 5.40k arrow right over r_1 arrow right over r_2

At t = 0, force (\(\vec{F}=(-5.00 \hat{\mathrm{i}}+5.00 \hat{\mathrm{j}}+4.00 \hat{\mathrm{k}})\) N begins to act on a 2.00 kg particle with an initial speed of 4.00 m/s. What is the particle’s speed when its displacement from the initial point is \(\vec{d}=(2.00 \hat{\mathrm{i}}+2.00 \hat{\mathrm{j}}+7.00 \hat{\mathrm{k}})\) m? Text Transcription: arrow right over F = (?5.00i + 5.00j + 4.00k) arrow right over d= (2.00i + 2.00j + 7.00k)

An initially stationary 2.0 kg object accelerates horizontally and uniformly to a speed of 10 m/s in 3.0 s. (a) In that 3.0 s interval, how much work is done on the object by the force accelerating it? What is the instantaneous power due to that force (b) at the end of the interval and (c) at the end of the first half of the interval?

A frightened child is restrained by her mother as the child slides down a frictionless playground slide. If the force on the child from the mother is 100 N up the slide, the child’s kinetic energy increases by 30 J as she moves down the slide a distance of 1.8 m. (a) How much work is done on the child by the gravitational force during the 1.8 m descent? (b) If the child is not restrained by her mother, how much will the child’s kinetic energy increase as she comes down the slide that same distance of 1.8 m?

If a car of mass 1200 kg is moving along a highway at 120 km/h, what is the car’s kinetic energy as determined by someone standing alongside the highway?

If a ski lift raises 100 passengers averaging 660 N in weight to a height of 150 m in 60.0 s, at constant speed, what average power is required of the force making the lift?

What is the power of the force required to move a 4500 kg elevator cab with a load of 1800 kg upward at constant speed 3.80 m/s?

A 45 kg block of ice slides down a frictionless incline 1.5 m long and 0.91 m high. A worker pushes up against the ice, parallel to the incline, so that the block slides down at constant speed. (a) Find the magnitude of the worker’s force. How much work is done on the block by (b) the worker’s force, (c) the gravitational force on the block, (d) the normal force on the block from the surface of the incline, and (e) the net force on the block?

A 4.00 kg block is pulled up a frictionless inclined plane by a 50.0 N force that is parallel to the plane, starting from rest. The normal force on the block from the plane has magnitude 13.41 N. What is the block’s speed when its displacement up the ramp is 3.00 m?

A spring with a spring constant of 18.0 N/cm has a cage attached to its free end. (a) How much work does the spring force do on the cage when the spring is stretched from its relaxed length by 7.60 mm? (b) How much additional work is done by the spring force when the spring is stretched by an additional 7.60 mm?