Problem 13
A large crate sits on the floor of a warehouse. Paul and Bob apply constant horizontal forces to the crate. The force applied by Paul has magnitude 48.0 N and direction 61.0\(^\circ\) south of west. How much work does Paul's force do during a displacement of the crate that is 12.0 m in the direction 22.0\(^\circ\) east of north?
Problem 14
You apply a constant force \(\overrightarrow{F} =(-68.0 \, \mathrm{N})\hat{\imath} +(36.0 \, \mathrm{N})\hat{\jmath}\) to a 380-kg car as the car travels 48.0 m in a direction that is 240.0\(^\circ\) counterclockwise from the +\(x\)-axis. How much work does the force you apply do on the car?
Problem 15
On a farm, you are pushing on a stubborn pig with a constant horizontal force with magnitude 30.0 N and direction 37.0\(^\circ\) counterclockwise from the +\(x\)-axis. How much work does this force do during a displacement of the pig that is (a) \(\overrightarrow{s} = (5.00 \, \mathrm{m})\hat{\imath}\); (b) \(\overrightarrow{s} = - (6.00 \, \mathrm{m})\hat{\jmath}\); (c) \(\overrightarrow{s} = - (2.00 \, \mathrm{m})\hat{\jmath} + (4.00 \, \mathrm{m}) \hat{\jmath}\)?
Problem 16
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. (a) How much work was done on the book between \(A\) and \(B\)? (b) If \(-\)0.750 J of work is done on the book from \(B\) to \(C\), how fast is it moving at point \(C\)? (c) How fast would it be moving at \(C\) if \(+\)0.750 J of work was done on it from \(B\) to \(C\)?
Problem 17
Adult cheetahs, the fastest of the great cats, have a mass of about 70 kg and have been clocked to run at up to 72 mi/h (32 m/s). (a) How many joules of kinetic energy does such a swift cheetah have? (b) By what factor would its kinetic energy change if its speed were doubled?
Problem 18
(a) In the Bohr model of the atom, the ground state electron in hydrogen has an orbital speed of 2190 km/s. What is its kinetic energy? (Consult Appendix F.) (b) If you drop a 1.0-kg weight (about 2 lb) from a height of 1.0 m, how many joules of kinetic energy will it have when it reaches the ground? (c) Is it reasonable that a 30-kg child could run fast enough to have 100 J of kinetic energy?
Problem 19
About 50,000 years ago, a meteor crashed into the earth near present-day Flagstaff, Arizona. Measurements from 2005 estimate that this meteor had a mass of about 1.4 \(\times\) 10\(^8\) kg (around 150,000 tons) and hit the ground at a speed of 12 km/s. (a) How much kinetic energy did this meteor deliver to the ground? (b) How does this energy compare to the energy released by a 1.0-megaton nuclear bomb? (A megaton bomb releases the same amount of energy as a million tons of TNT, and 1.0 ton of TNT releases 4.184 \(\times\) 10\(^9\) J of energy.)
Problem 20
A 4.80-kg watermelon is dropped from rest from the roof of an 18.0-m-tall building and feels no appreciable air resistance. (a) Calculate the work done by gravity on the watermelon during its displacement from the roof to the ground. (b) Just before it strikes the ground, what is the watermelon's (i) kinetic energy and (ii) speed? (c) Which of the answers in parts (a) and (b) would be \(different\) if there were appreciable air resistance?
Problem 21
Use the work\(-\)energy theorem to solve each of these problems. You can use Newton's laws to check your answers. Neglect air resistance in all cases. (a) A branch falls from the top of a 95.0-m-tall redwood tree, starting from rest. How fast is it moving when it reaches the ground? (b) A volcano ejects a boulder directly upward 525 m into the air. How fast was the boulder moving just as it left the volcano?
Problem 22
Use the work\(-\)energy theorem to solve each of these problems. You can use Newton's laws to check your answers. (a) A skier moving at 5.00 m/s encounters a long, rough horizontal patch of snow having a coefficient of kinetic friction of 0.220 with her skis. How far does she travel on this patch before stopping? (b) Suppose the rough patch in part (a) was only 2.90 m long. How fast would the skier be moving when she reached the end of the patch? (c) At the base of a frictionless icy hill that rises at 25.0\(^\circ\) above the horizontal, a toboggan has a speed of 12.0 m/s toward the hill. How high vertically above the base will it go before stopping?
