Math / Algebra

Question2. (4 punti)
Una gru, il cui motore ha una potenza di $3,00 \mathrm{~kW}$ , solleva di $10,4 \mathrm{~m}$ , a velocità costante, un carico che ha massa di 359 kg . Calcola il tempo impiegato dalla gru per sollevare il carico.

Studdy Solution

STEP 1

1. The crane's motor has a power of $3.00 \, \text{kW}$ .
2. The crane lifts a load with a mass of $359 \, \text{kg}$ .
3. The load is lifted a height of $10.4 \, \text{m}$ .
4. The lifting is done at a constant speed.
5. We need to calculate the time taken to lift the load.

STEP 2

1. Convert power from kilowatts to watts.
2. Calculate the gravitational force on the load.
3. Calculate the work done in lifting the load.
4. Use the power formula to find the time taken.

STEP 3

Convert the power from kilowatts to watts.
Given power in kilowatts is $3.00 \, \text{kW}$ . $\text{Power in watts} = 3.00 \times 1000 = 3000 \, \text{W}$

STEP 4

Calculate the gravitational force on the load.
The gravitational force $F$ is given by: $F = m \cdot g$ where $m = 359 \, \text{kg}$ and $g = 9.81 \, \text{m/s}^2$ .
$F = 359 \times 9.81 = 3521.79 \, \text{N}$

STEP 5

Calculate the work done in lifting the load.
Work done $W$ is given by: $W = F \cdot h$ where $h = 10.4 \, \text{m}$ .
$W = 3521.79 \times 10.4 = 36626.616 \, \text{J}$

STEP 6

Use the power formula to find the time taken.
Power $P$ is given by: $P = \frac{W}{t}$ Rearranging for time $t$ : $t = \frac{W}{P}$
Substitute the known values: $t = \frac{36626.616}{3000}$
$t = 12.208872 \, \text{s}$
Rounding to three significant figures, the time taken is: $\boxed{12.2 \, \text{s}}$

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Question2. (4 punti)
Una gru, il cui motore ha una potenza di $3,00 \mathrm{~kW}$ , solleva di $10,4 \mathrm{~m}$ , a velocità costante, un carico che ha massa di 359 kg . Calcola il tempo impiegato dalla gru per sollevare il carico.

Studdy Solution

STEP 1

1. The crane's motor has a power of $3.00 \, \text{kW}$ .
2. The crane lifts a load with a mass of $359 \, \text{kg}$ .
3. The load is lifted a height of $10.4 \, \text{m}$ .
4. The lifting is done at a constant speed.
5. We need to calculate the time taken to lift the load.

STEP 2

1. Convert power from kilowatts to watts.
2. Calculate the gravitational force on the load.
3. Calculate the work done in lifting the load.
4. Use the power formula to find the time taken.

STEP 3

Convert the power from kilowatts to watts.
Given power in kilowatts is $3.00 \, \text{kW}$ . $\text{Power in watts} = 3.00 \times 1000 = 3000 \, \text{W}$

STEP 4

Calculate the gravitational force on the load.
The gravitational force $F$ is given by: $F = m \cdot g$ where $m = 359 \, \text{kg}$ and $g = 9.81 \, \text{m/s}^2$ .
$F = 359 \times 9.81 = 3521.79 \, \text{N}$

STEP 5

Calculate the work done in lifting the load.
Work done $W$ is given by: $W = F \cdot h$ where $h = 10.4 \, \text{m}$ .
$W = 3521.79 \times 10.4 = 36626.616 \, \text{J}$

STEP 6

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Question2. (4 punti)Una gru, il cui motore ha una potenza di 3,00 kW3,00 \mathrm{~kW}3,00 kW, solleva di 10,4 m10,4 \mathrm{~m}10,4 m, a velocità costante, un carico che ha massa di 359 kg . Calcola il tempo impiegato dalla gru per sollevare il carico.

Studdy Solution

STEP 1

1. The crane's motor has a power of 3.00 kW3.00 \, \text{kW}3.00kW.2. The crane lifts a load with a mass of 359 kg359 \, \text{kg}359kg.3. The load is lifted a height of 10.4 m10.4 \, \text{m}10.4m.4. The lifting is done at a constant speed.5. We need to calculate the time taken to lift the load.

STEP 2

1. Convert power from kilowatts to watts.2. Calculate the gravitational force on the load.3. Calculate the work done in lifting the load.4. Use the power formula to find the time taken.

STEP 3

Convert the power from kilowatts to watts.Given power in kilowatts is 3.00 kW3.00 \, \text{kW}3.00kW. Power in watts=3.00×1000=3000 W \text{Power in watts} = 3.00 \times 1000 = 3000 \, \text{W} Power in watts=3.00×1000=3000W

STEP 4

Calculate the gravitational force on the load.The gravitational force F F F is given by: F=m⋅g F = m \cdot g F=m⋅g where m=359 kg m = 359 \, \text{kg} m=359kg and g=9.81 m/s2 g = 9.81 \, \text{m/s}^2 g=9.81m/s2.F=359×9.81=3521.79 N F = 359 \times 9.81 = 3521.79 \, \text{N} F=359×9.81=3521.79N

STEP 5

Calculate the work done in lifting the load.Work done W W W is given by: W=F⋅h W = F \cdot h W=F⋅h where h=10.4 m h = 10.4 \, \text{m} h=10.4m.W=3521.79×10.4=36626.616 J W = 3521.79 \times 10.4 = 36626.616 \, \text{J} W=3521.79×10.4=36626.616J

STEP 6

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Studdy solves anything!

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Question2. (4 punti)
Una gru, il cui motore ha una potenza di $3,00 \mathrm{~kW}$ , solleva di $10,4 \mathrm{~m}$ , a velocità costante, un carico che ha massa di 359 kg . Calcola il tempo impiegato dalla gru per sollevare il carico.

1. The crane's motor has a power of $3.00 \, \text{kW}$ .
2. The crane lifts a load with a mass of $359 \, \text{kg}$ .
3. The load is lifted a height of $10.4 \, \text{m}$ .
4. The lifting is done at a constant speed.
5. We need to calculate the time taken to lift the load.

1. Convert power from kilowatts to watts.
2. Calculate the gravitational force on the load.
3. Calculate the work done in lifting the load.
4. Use the power formula to find the time taken.

Convert the power from kilowatts to watts.
Given power in kilowatts is $3.00 \, \text{kW}$ . $\text{Power in watts} = 3.00 \times 1000 = 3000 \, \text{W}$

Calculate the gravitational force on the load.
The gravitational force $F$ is given by: $F = m \cdot g$ where $m = 359 \, \text{kg}$ and $g = 9.81 \, \text{m/s}^2$ .
$F = 359 \times 9.81 = 3521.79 \, \text{N}$

Calculate the work done in lifting the load.
Work done $W$ is given by: $W = F \cdot h$ where $h = 10.4 \, \text{m}$ .
$W = 3521.79 \times 10.4 = 36626.616 \, \text{J}$