Concept #1: Power

Practice: A 350 g mass can undergo two different motions, propelled by gravity in each case: it can either fall a height of 10 cm, or it can slide down a frictionless incline at a 30° angle. In which case is the mass’ kinetic energy changing faster?

Air resistance at high speed is often given as Fair = bv2. If the terminal velocity of a 75 kg skydiver is 60 m/s, at what rate is the air resistance sapping the skydiver’s kinetic energy?

A car moves at a speed of 25 m/s. If the car were to experience 4.5 kN of air resistance at this speed, how much power would the engine need to produce to keep the car moving at a constant speed?

A 10 kg object slides along a surface with a coefficient of kinetic friction of 0.3, moving with an initial velocity of 20 m/s. What is the average thermal power generated as the object slows to a stop?

How much work must you do to push a 12.0 kg block of steel across a steel table (μk=0.6) at a steady speed of 1.20 m/s for 5.80 s? What is your power output while doing so?

It is 6.00 km from your home to the physics lab. As part of your physical fitness program, you could run that distance at 10.0 km/hr (which uses up energy at the rate of 700 W), or you could walk it leisurely at 3.00 km/hr (which uses energy at 290 W).(a) Which choice would burn up more energy?(b) Why is it that the more intense exercise actually burns up less energy than the less intense one?(c) How much energy (in joules) would it burn?

(a) How much energy is consumed by a 1.2 kW hair dryer used for 12 min?(b) How much energy is consumed by a 11 W night light left on for 18 hr?

An 820-N Marine in basic training climbs a 12.0-m vertical rope at a constant speed in 8.00 s. What is his power output?

During a workout, football players ran up the stadium stairs in 80 s. The stairs are 83 m long and inclined at an angle of 31 degrees. If a player has a mass of 87 kg, estimate his average power output on the way up. Ignore friction and air resistance.

A bicyclist coasts down a 6.5 degree hill at a steady speed of 4.5 m/s. Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclists power output to climb the same hill at the same speed?

A test car of mass 740 kg is moving at a speed of 7.3 m/s when it crashes into a wall to test its bumper. If the car comes to rest in 0.36 s, how much average power is expended in the process?
1. 42820.9
2. 47940.6
3. 59118.6
4. 49662.2
5. 50789.2
6. 54770.3
7. 45825.2
8. 44990.3
9. 46540.4
10. 51904.1

Four students run up the stairs as shown in the figure: Adam (mass of 80 kg) goes up 10 m in 10 s, Bob (80 kg) 10 m in 8 seconds, Claire (64 kg) 10 m in 8 s, and David (80 kg) 20 m in 25 s.
Who has the smallest power output?
A. Bob
B. Claire
C. David
D. Adam