Chapter 6: Work and Energy

You have two springs that are identical except that spring 1 is stiffer than spring 2 \(\left( {{k_{\bf{1}}}{\bf{ > }}{k_{\bf{2}}}} \right)\). On which spring is more work done: (a) if they are stretched using the same force; (b) if they are stretched the same distance?

A ball is thrown straight up. At what point does the ball have the most energy? Ignore air resistance.

1. At the highest point of its path.
2. When it is first thrown.
3. Just before it hits the ground.
4. When the ball is halfway to the highest point of its path.
5. Everywhere; the energy of the ball is the same at all of these points.

(II) During a workout, football players ran up the stadium stairs in 75 s. The distance along the stairs is 83 m and they are inclined at a 33° angle. If a player has a mass of 82 kg, estimate his average power output on the way up. Ignore friction and air resistance.

(II) Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a force of about 15 N.

If the speed of a particle triples, by what factor does its kinetic energy increase?

A car accelerates from rest to\[30\;{\rm{km/h}}\]. Later, on a highway it accelerates from\[30\;{\rm{km/h}}\] to\[60\;{\rm{km/h}}\]. Which takes more energy, going from 0 to 30, or from 30 to 60?

1. 0 to\[30\;{\rm{km/h}}\] .
2. 30 to\[60\;{\rm{km/h}}\].
3. Both are the same.

(III) When using a mercury barometer (Section 10–6), the vapor pressure of mercury is usually assumed to be zero. At room temperature mercury's vapor pressure is about 0.0015 mm-Hg. At sea level, the height h of mercury in a barometer is about 760 mm. (a) If the vapor pressure of mercury is neglected, is the true atmospheric pressure greater or less than the value read from the barometer? (b) What is the percent error? (c) What is the percent error if you use a water barometer and ignore water's saturated vapor pressure at STP?

(II) A pump lifts 27.0 kg of water per minute through a height of 3.50 m. What minimum output rating (watts) must the pump motor have?

Question: (II) A person of mass 75 kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia\({\bf{820}}\;{\bf{kg}} \cdot {{\bf{m}}^{\bf{2}}}\). The platform rotates without friction with angular velocity\({\bf{0}}{\bf{.95}}\;{{{\bf{rad}}} \mathord{\left/{\vphantom {{{\bf{rad}}} {\bf{s}}}} \right.} {\bf{s}}}\). The person walks radially to the edge of the platform. (a) Calculate the angular velocity when the person reaches the edge. (b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.

(II) In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.40 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?