Answer :
We are given two separate problems that involve calculating power as the amount of energy (or work) divided by the time taken.
For the toaster oven:
1. The toaster oven uses an energy of
[tex]$$
E = 67\,500 \text{ joules}
$$[/tex]
in a time of
[tex]$$
t = 45 \text{ seconds}.
$$[/tex]
2. Power is defined as the energy divided by the time. Therefore, the power of the oven is given by
[tex]$$
P = \frac{E}{t} = \frac{67\,500 \text{ J}}{45 \text{ s}} = 1500 \text{ watts}.
$$[/tex]
For the horse:
1. The horse moves a sleigh a distance of
[tex]$$
d = 1.00 \text{ kilometer} = 1000 \text{ meters}.
$$[/tex]
2. A horizontal force of
[tex]$$
F = 2000 \text{ newtons}
$$[/tex]
is applied to the harness.
3. The work performed by the horse is found by multiplying the force by the distance:
[tex]$$
W = F \times d = 2000 \text{ N} \times 1000 \text{ m} = 2\,000\,000 \text{ joules}.
$$[/tex]
4. The time given is 45 minutes. We first convert this to seconds:
[tex]$$
t = 45 \text{ minutes} \times 60 \frac{\text{seconds}}{\text{minute}} = 2700 \text{ seconds}.
$$[/tex]
5. The power produced by the horse is then calculated by dividing the work done by the time:
[tex]$$
P = \frac{W}{t} = \frac{2\,000\,000 \text{ J}}{2700 \text{ s}} \approx 740.74 \text{ watts}.
$$[/tex]
Thus, the final answers are:
- The toaster oven has a power of [tex]$\displaystyle 1500 \text{ watts}$[/tex].
- The horse produces a power of approximately [tex]$\displaystyle 740.74 \text{ watts}$[/tex].
For the toaster oven:
1. The toaster oven uses an energy of
[tex]$$
E = 67\,500 \text{ joules}
$$[/tex]
in a time of
[tex]$$
t = 45 \text{ seconds}.
$$[/tex]
2. Power is defined as the energy divided by the time. Therefore, the power of the oven is given by
[tex]$$
P = \frac{E}{t} = \frac{67\,500 \text{ J}}{45 \text{ s}} = 1500 \text{ watts}.
$$[/tex]
For the horse:
1. The horse moves a sleigh a distance of
[tex]$$
d = 1.00 \text{ kilometer} = 1000 \text{ meters}.
$$[/tex]
2. A horizontal force of
[tex]$$
F = 2000 \text{ newtons}
$$[/tex]
is applied to the harness.
3. The work performed by the horse is found by multiplying the force by the distance:
[tex]$$
W = F \times d = 2000 \text{ N} \times 1000 \text{ m} = 2\,000\,000 \text{ joules}.
$$[/tex]
4. The time given is 45 minutes. We first convert this to seconds:
[tex]$$
t = 45 \text{ minutes} \times 60 \frac{\text{seconds}}{\text{minute}} = 2700 \text{ seconds}.
$$[/tex]
5. The power produced by the horse is then calculated by dividing the work done by the time:
[tex]$$
P = \frac{W}{t} = \frac{2\,000\,000 \text{ J}}{2700 \text{ s}} \approx 740.74 \text{ watts}.
$$[/tex]
Thus, the final answers are:
- The toaster oven has a power of [tex]$\displaystyle 1500 \text{ watts}$[/tex].
- The horse produces a power of approximately [tex]$\displaystyle 740.74 \text{ watts}$[/tex].
