9. Work & Energy

A pendulum is made by tying a 500 g ball to a 75-cm-long string. The pendulum is pulled 30° to one side, then released. What is the ball's speed at the lowest point of its trajectory?

A 2.0-kg block slides across a rough surface with a constant coefficient of kinetic friction of 0.50 (Fig. 7–38a). The block starts at x= 0 with an initial velocity of 4.9 m/s. Pushing the block is a force directed at 36.8° below the horizontal and whose magnitude increases with position as shown in Fig. 7–38b.

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(d) Draw a line on the graph showing the magnitude of the friction force versus distance x.

FIGURE EX9.20 is the force-versus-position graph for a particle moving along the x-axis. Determine the work done on the particle during each of the three intervals 0–1 m, 1–2 m, and 2–3 m.

Which of the following sets of information would a student need to calculate the net work done on an object according to the work-energy theorem?

A crate of mass $m$ is pulled across a horizontal floor by a constant force $F$ at an angle $\theta$ above the horizontal. The coefficient of kinetic friction between the crate and the floor is $\mu$. What is the net force acting on the crate in the horizontal direction?

A 50 kg ice skater is gliding along the ice, heading due north at 4.0 m/s. The ice has a small coefficient of static friction, to prevent the skater from slipping sideways, but μ_k = 0. Suddenly, a wind from the northeast exerts a force of 4.0 N on the skater. What is the minimum value of μ_s that allows her to continue moving straight north?

A 3.5-kg object moving in two dimensions initially has a velocity ${\overrightarrow{v_1}}_{}$ = (10.0 î + 20.0 ĵ) m/s. A net force $\overrightarrow{F}$ then acts on the object for 2.0 s, after which the object’s velocity is ${\overrightarrow{v_2}}_{}$ = (15.0 î + 30.0 ĵ) m/s. Determine the work done by $\overrightarrow{F}$ on the object.

(II) An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow?

A $1.50$-kg book is sliding along a rough horizontal surface. At point $A$ it is moving at $3.21$ m/s, and at point $B$ it has slowed to $1.25$ m/s. How much work was done on the book between $A$ and $B$?

Justin, with a mass of 30 kg, is going down an 8.0-m-high water slide. He starts at rest, and his speed at the bottom is 11 m/s. How much thermal energy is created by friction during his descent?

A ball shot straight up with kinetic energy K₀ reaches height h. What height will it reach if the initial kinetic energy is doubled?

(II) A 66.5-kg hiker starts at an elevation of 1150 m and climbs to the top of a peak 2660 m high. Can the actual work done be greater than this? Explain.

A horizontal spring with spring constant 750 N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it 5.0 cm. How hard is the athlete pushing?

In the context of the work-energy theorem, which of the following best describes the net force acting on an object?