Answer :
Sure! Let's go through each of the questions and explain the solutions in a clear and easy way.
1. If a kitchen blender can perform 3,200 joules of work in 16 seconds, what is its power?
Power is calculated using the formula:
[tex]\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \][/tex]
Here, the work done is 3,200 joules and the time is 16 seconds.
[tex]\[ \text{Power} = \frac{3200 \, \text{joules}}{16 \, \text{seconds}} = 200 \, \text{watts} \][/tex]
2. Consider a set of pulleys that was used to lift a piano weighing 1,000 newtons upwards by 3 meters over the course of 20 seconds. How much power was used?
First, calculate the work done, which is the product of the force and the distance:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} = 1000 \, \text{newtons} \times 3 \, \text{meters} = 3000 \, \text{joules} \][/tex]
Now, calculate the power:
[tex]\[ \text{Power} = \frac{3000 \, \text{joules}}{20 \, \text{seconds}} = 150 \, \text{watts} \][/tex]
3. If a force of 50 newtons is used to push a box a distance of 6 meters in 3 seconds, how much power is used?
Calculate the work done first:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} = 50 \, \text{newtons} \times 6 \, \text{meters} = 300 \, \text{joules} \][/tex]
Then, calculate the power:
[tex]\[ \text{Power} = \frac{300 \, \text{joules}}{3 \, \text{seconds}} = 100 \, \text{watts} \][/tex]
4. If a 500-watt microwave oven runs for 3 minutes, how much work is done?
First, convert the time from minutes to seconds: [tex]\(3 \, \text{minutes} = 3 \times 60 = 180 \, \text{seconds}\)[/tex].
Calculate the work done as follows:
[tex]\[ \text{Work} = \text{Power} \times \text{Time} = 500 \, \text{watts} \times 180 \, \text{seconds} = 90,000 \, \text{joules} \][/tex]
5. If a 60-watt light bulb is on for 20 minutes, how much work is done?
Convert the time from minutes to seconds: [tex]\(20 \, \text{minutes} = 20 \times 60 = 1200 \, \text{seconds}\)[/tex].
Calculate the work done:
[tex]\[ \text{Work} = \text{Power} \times \text{Time} = 60 \, \text{watts} \times 1200 \, \text{seconds} = 72,000 \, \text{joules} \][/tex]
6. If a 60-watt light bulb uses 432,000 joules, how long was it on for?
Time is calculated using the formula:
[tex]\[ \text{Time} = \frac{\text{Work}}{\text{Power}} \][/tex]
[tex]\[ \text{Time} = \frac{432,000 \, \text{joules}}{60 \, \text{watts}} = 7,200 \, \text{seconds} \][/tex]
These are the correct solutions for each question!
1. If a kitchen blender can perform 3,200 joules of work in 16 seconds, what is its power?
Power is calculated using the formula:
[tex]\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \][/tex]
Here, the work done is 3,200 joules and the time is 16 seconds.
[tex]\[ \text{Power} = \frac{3200 \, \text{joules}}{16 \, \text{seconds}} = 200 \, \text{watts} \][/tex]
2. Consider a set of pulleys that was used to lift a piano weighing 1,000 newtons upwards by 3 meters over the course of 20 seconds. How much power was used?
First, calculate the work done, which is the product of the force and the distance:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} = 1000 \, \text{newtons} \times 3 \, \text{meters} = 3000 \, \text{joules} \][/tex]
Now, calculate the power:
[tex]\[ \text{Power} = \frac{3000 \, \text{joules}}{20 \, \text{seconds}} = 150 \, \text{watts} \][/tex]
3. If a force of 50 newtons is used to push a box a distance of 6 meters in 3 seconds, how much power is used?
Calculate the work done first:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} = 50 \, \text{newtons} \times 6 \, \text{meters} = 300 \, \text{joules} \][/tex]
Then, calculate the power:
[tex]\[ \text{Power} = \frac{300 \, \text{joules}}{3 \, \text{seconds}} = 100 \, \text{watts} \][/tex]
4. If a 500-watt microwave oven runs for 3 minutes, how much work is done?
First, convert the time from minutes to seconds: [tex]\(3 \, \text{minutes} = 3 \times 60 = 180 \, \text{seconds}\)[/tex].
Calculate the work done as follows:
[tex]\[ \text{Work} = \text{Power} \times \text{Time} = 500 \, \text{watts} \times 180 \, \text{seconds} = 90,000 \, \text{joules} \][/tex]
5. If a 60-watt light bulb is on for 20 minutes, how much work is done?
Convert the time from minutes to seconds: [tex]\(20 \, \text{minutes} = 20 \times 60 = 1200 \, \text{seconds}\)[/tex].
Calculate the work done:
[tex]\[ \text{Work} = \text{Power} \times \text{Time} = 60 \, \text{watts} \times 1200 \, \text{seconds} = 72,000 \, \text{joules} \][/tex]
6. If a 60-watt light bulb uses 432,000 joules, how long was it on for?
Time is calculated using the formula:
[tex]\[ \text{Time} = \frac{\text{Work}}{\text{Power}} \][/tex]
[tex]\[ \text{Time} = \frac{432,000 \, \text{joules}}{60 \, \text{watts}} = 7,200 \, \text{seconds} \][/tex]
These are the correct solutions for each question!
