Question

physical science - power practice problems

1. if a runners power is 400 w, as she runs, how much chemical energy does she convert into other forms in 10.0 min?
2. one horsepower is a unit of power equal to 746 w. how much energy can a 150 horsepower engine transform in 10 s?
3. a person exerts a force of 500 n on a box, pushing it across the floor 25 m. he completes his work in exactly 30 seconds. what is the amount of power the person expended?
4. how much work is done using a 500 - watt microwave oven for 5 minutes.
5. a set of pulleys is used to lift a piano with a mass of 102 kg. the piano is lifted 3 meters in 1 minutes. how much power is used?

Explanation:

Problem 1

Step1: Convert time to seconds

We know that \(1\) minute \( = 60\) seconds. So, \(t=10.0\) min \(=10\times60 = 600\) s.

Step2: Use the power formula \(P=\frac{W}{t}\) (where \(W\) is work/energy and \(P\) is power)

Rearrange for \(W\): \(W = P\times t\). Given \(P = 400\) W and \(t = 600\) s. Then \(W=400\times600\)

$$W = 240000\space J$$

Step1: Find the power of the engine

If \(1\) horsepower \(=746\) W, then for a \(150\) - horsepower engine, \(P=150\times746\) W \(= 111900\) W

Step2: Use the formula \(W = P\times t\)

Given \(t = 10\) s and \(P=111900\) W. Then \(W=111900\times10\)

$$W=1119000\space J$$

Step1: Calculate the work done

Use the formula \(W = F\times d\) (where \(F\) is force and \(d\) is distance). Given \(F = 500\) N and \(d = 25\) m. So \(W=500\times25=12500\) J

Step2: Calculate the power

Use the formula \(P=\frac{W}{t}\). Given \(W = 12500\) J and \(t = 30\) s. Then \(P=\frac{12500}{30}\approx416.67\) W

Answer:

\(240000\space J\)

Problem 2