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Answer :
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Question 21:
A 900 Watt crane is pulling a 500N piece of metal to the top of a 20m tall building. We need to find out how long it will take and how fast the piece of metal will be moving.
1. Calculate the Work Done:
Work done (W) is given by the formula:
[tex]\[
W = \text{Force} \times \text{Distance}
\][/tex]
Here, Force = 500 N and Distance = 20 m.
[tex]\[
W = 500 \, \text{N} \times 20 \, \text{m} = 10,000 \, \text{Joules}
\][/tex]
2. Calculate the Time Taken:
Power (P) is the rate at which work is done and is given by:
[tex]\[
P = \frac{W}{t}
\][/tex]
Rearrange to find time (t):
[tex]\[
t = \frac{W}{P} = \frac{10,000 \, \text{Joules}}{900 \, \text{Watts}} \approx 11.11 \, \text{seconds}
\][/tex]
3. Calculate the Speed of the Metal:
To find the speed, we use the relation:
[tex]\[
P = \text{Force} \times \text{Speed}
\][/tex]
Rearrange to find speed:
[tex]\[
\text{Speed} = \frac{P}{\text{Force}} = \frac{900 \, \text{Watts}}{500 \, \text{N}} = 1.8 \, \text{m/s}
\][/tex]
Question 22:
Gino builds a toy machine that does 568 J of work every 45 seconds. We need to calculate the power it generates and the speed with which it can move a 5 kg block.
1. Calculate the Power Generated:
Power (P) is calculated by:
[tex]\[
P = \frac{W}{t}
\][/tex]
Here, Work (W) = 568 Joules and Time (t) = 45 seconds.
[tex]\[
P = \frac{568 \, \text{Joules}}{45 \, \text{seconds}} \approx 12.62 \, \text{Watts}
\][/tex]
2. Calculate the Speed:
Use the formula for power:
[tex]\[
P = \text{Force} \times \text{Speed}
\][/tex]
Force can be calculated using [tex]\(\text{Force} = \text{mass} \times \text{gravity}\)[/tex]. Here, mass = 5 kg and gravity ≈ 9.81 m/s².
[tex]\[
\text{Force} = 5 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 49.05 \, \text{N}
\][/tex]
Rearrange the power formula for speed:
[tex]\[
\text{Speed} = \frac{P}{\text{Force}} = \frac{12.62 \, \text{Watts}}{49.05 \, \text{N}} \approx 0.257 \, \text{m/s}
\][/tex]
I hope this helps! Let me know if you have any more questions.
Question 21:
A 900 Watt crane is pulling a 500N piece of metal to the top of a 20m tall building. We need to find out how long it will take and how fast the piece of metal will be moving.
1. Calculate the Work Done:
Work done (W) is given by the formula:
[tex]\[
W = \text{Force} \times \text{Distance}
\][/tex]
Here, Force = 500 N and Distance = 20 m.
[tex]\[
W = 500 \, \text{N} \times 20 \, \text{m} = 10,000 \, \text{Joules}
\][/tex]
2. Calculate the Time Taken:
Power (P) is the rate at which work is done and is given by:
[tex]\[
P = \frac{W}{t}
\][/tex]
Rearrange to find time (t):
[tex]\[
t = \frac{W}{P} = \frac{10,000 \, \text{Joules}}{900 \, \text{Watts}} \approx 11.11 \, \text{seconds}
\][/tex]
3. Calculate the Speed of the Metal:
To find the speed, we use the relation:
[tex]\[
P = \text{Force} \times \text{Speed}
\][/tex]
Rearrange to find speed:
[tex]\[
\text{Speed} = \frac{P}{\text{Force}} = \frac{900 \, \text{Watts}}{500 \, \text{N}} = 1.8 \, \text{m/s}
\][/tex]
Question 22:
Gino builds a toy machine that does 568 J of work every 45 seconds. We need to calculate the power it generates and the speed with which it can move a 5 kg block.
1. Calculate the Power Generated:
Power (P) is calculated by:
[tex]\[
P = \frac{W}{t}
\][/tex]
Here, Work (W) = 568 Joules and Time (t) = 45 seconds.
[tex]\[
P = \frac{568 \, \text{Joules}}{45 \, \text{seconds}} \approx 12.62 \, \text{Watts}
\][/tex]
2. Calculate the Speed:
Use the formula for power:
[tex]\[
P = \text{Force} \times \text{Speed}
\][/tex]
Force can be calculated using [tex]\(\text{Force} = \text{mass} \times \text{gravity}\)[/tex]. Here, mass = 5 kg and gravity ≈ 9.81 m/s².
[tex]\[
\text{Force} = 5 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 49.05 \, \text{N}
\][/tex]
Rearrange the power formula for speed:
[tex]\[
\text{Speed} = \frac{P}{\text{Force}} = \frac{12.62 \, \text{Watts}}{49.05 \, \text{N}} \approx 0.257 \, \text{m/s}
\][/tex]
I hope this helps! Let me know if you have any more questions.
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