Conceptual Physics

6.7 - Interactive problem: work-kinetic energy theorem

In this simulation, you are a skier and your challenge is to do the correct amount of work to build up enough energy to soar over the canyon and land near the lip of the slope on the right. You, a 50.0 kg skier, have a flat 12.0 meter long runway leading up to the lip of the canyon. In that stretch, you must apply a force such that at the end of the straightaway, you are traveling with a speed of 8.00 m/s. Any slower, and your jump will fall short. Any faster, and you will overshoot. How much force must you apply, in newtons, over the 12.0 meter flat stretch? Ignore other forces like friction and air resistance.

Enter the force, to the nearest newton, in the entry box and press GO to check your result. If you have trouble with this problem, review the section on the work-kinetic energy theorem. (If you want to, you can check your answer using a linear motion equation and Newton’s second law.)

6.8 - Interactive checkpoint: a spaceship

A 45,500 kg spaceship is far from any

significant source of gravity. It

accelerates at a constant rate from

13,100 m/s to 15,700 m/s over a

distance of 2560 km. What is the

magnitude of the force on the ship

due to the action of its engines? Use

equations involving work and energy

to solve the problem, and assume

that the mass is constant.

Answer:

F = N

6.9 - Power

Power: Work divided by time; also the rate of

energy output or consumption.

The definition of work í the dot product of force and displacement í does not say anything about how long it takes for the work to occur. It might take a second, or a year, or any interval of time. Power adds the concept of time to the topics of work and energy. Power equals the amount of work divided by the time it took to do the work. You see this expressed as an equation in Equation 1.

One reason we care about power is because more power means that work can be accomplished faster. Would you rather have a car that accelerated you from zero to 100 kilometers per hour in five seconds, or five minutes? (Some of us have owned cars of the latter type.)

The unit of power is the watt (W), which equals one joule per second. It is a scalar unit. Power can also be expressed as the rate of change of energy. For instance, a 100 megawatt power plant supplies 100 million joules of energy to the electric grid every second. Sometimes power is expressed in terms of an older unit, the horsepower. This unit comes from the days when scientists sought to establish a standard for how much work a horse could do in a set amount of time. They then compared the power of early engines to the power of a horse. One horsepower equals 550 foot-pounds/second, which is the same as 746 watts. We still measure the power of cars in horsepower. For instance, a 300-horsepower Porsche is more powerful than a 135-horsepower Toyota. The Porsche’s engine is capable of doing more work in a given period of time than the Toyota’s.

Power

Rate of work