Question

A hair dryer emits energy in the form of heat. If 48,000 Joules of energy (work) are emitted by the hair dryer each minute, what is the power of the hair dryer in watts? In horsepower?

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Gerhard

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Step 1: Power is defined as the rate at which work is done or energy is transferred, which can be calculated using the formula:

P = \dfrac{W}{t}

where:

P = power (in watts),

W = work or energy (in joules),

t = time (in seconds).

Step 2: Given that 48,000 Joules of energy are emitted by the hair dryer each minute (1 minute = 60 seconds), we can substitute these values into the formula to find the power in watts:

P = \dfrac{48,000}{60} = 800\text{ watts}

Step 3: To convert the power from watts to horsepower, we can use the conversion factor: 1 horsepower = 745.7 watts. So, we can calculate the power in horsepower:

P_{\text{hp}}=\dfrac{800}{745.7}\approx1.07\text{ horsepower}

Therefore, the power of the hair dryer is 800 watts and approximately 1.07 horsepower.

Answer: The power of the hair dryer is 800 watts and approximately 1.07 horsepower.

where:

Step 2: Given that 48,000 Joules of energy are emitted by the hair dryer each minute (1 minute = 60 seconds), we can substitute these values into the formula to find the power in watts:

Step 3: To convert the power from watts to horsepower, we can use the conversion factor: 1 horsepower = 745.7 watts. So, we can calculate the power in horsepower:

Therefore, the power of the hair dryer is 800 watts and approximately 1.07 horsepower.

Answer: The power of the hair dryer is 800 watts and approximately 1.07 horsepower.

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