Question

review and assess
checking concepts

1. define work in terms of energy.
2. how do you find an objects mechanical energy?
3. for each of the following, decide which forms of energy are present: a walnut falls from a tree; a spring is stretched.
4. an eagle flies from its perch in a tree to the ground to capture and eat its prey. describe its energy transformations.
5. how does energy become stored in a fossil fuel? what kind of energy is stored?

thinking critically

1. calculating find the power of a machine that transfers 450 j of energy in 9 s.
2. calculating a 1,350 - kg car travels at 12 m/s. what is its kinetic energy?
3. comparing and contrasting in the illustration below, which vehicle has the least kinetic energy? which has the greatest kinetic energy? explain your answers.
4. problem solving a 380 - n girl walks down a flight of stairs so that she is 2.5 m below her starting level. what is the change in the girls gravitational potential energy?
5. applying concepts one chef places a pie in the oven at a low setting so that it is baked in one hour. another chef places a pie in the

Explanation:

Step1: Recall power formula

Power $P=\frac{W}{t}$, where $W$ is work - energy transferred and $t$ is time.

Step2: Substitute given values

Given $W = 450\ J$ and $t=9\ s$. Then $P=\frac{450\ J}{9\ s}$.

Step3: Calculate power

$P = 50\ W$.

Step4: Recall kinetic - energy formula

The kinetic - energy formula is $K=\frac{1}{2}mv^{2}$, where $m$ is mass and $v$ is velocity.

Step5: Calculate kinetic energy of car

For a car with $m = 1350\ kg$ and $v = 12\ m/s$, $K=\frac{1}{2}\times1350\ kg\times(12\ m/s)^{2}=\frac{1}{2}\times1350\times144\ J=97200\ J$.

Step6: Analyze kinetic - energy for vehicles in 18

Since $K=\frac{1}{2}mv^{2}$ and velocity is the same ($v = 20\ m/s$) for all vehicles in the illustration, the vehicle with the greatest mass has the greatest kinetic energy and the vehicle with the least mass has the least kinetic energy.

Step7: Recall gravitational - potential - energy formula

The change in gravitational potential energy $\Delta U = mgh$. Here, the force $F = mg=380\ N$ and $h = 2.5\ m$. So $\Delta U=-Fh$ (negative because the height decreases).

Step8: Calculate change in gravitational potential energy

$\Delta U=-380\ N\times2.5\ m=- 950\ J$.

Answer:

1. $50\ W$
2. $97200\ J$
3. The vehicle with the greatest mass has the greatest kinetic energy and the vehicle with the least mass has the least kinetic energy when velocities are equal.
4. $-950\ J$