How much power is needed to lift a 75- kg student vertically upward at a constant speed of 0.33 m/s ?

Options

A. 12.5W
B. 115W
C. 242.5
D. 230W

Answer

To find the power needed to lift a 75 kg student vertically upward at a constant speed of 0.33 m/s, we can follow these steps:

### Step 1: Identify the Force Required
The force required to lift the student is equal to the weight of the student, which can be calculated using the formula:
\[ F = m \cdot g \]
where:
- \( m = 75 \, \text{kg} \) (mass of the student)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

### Step 2: Calculate the Weight
Now we can calculate the weight:
\[ F = 75 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \]
\[ F = 735 \, \text{N} \]

### Step 3: Use the Power Formula
Power is defined as the rate of doing work. When lifting an object at a constant speed, the power can be calculated using the formula:
\[ P = F \cdot v \]
where:
- \( P \) = power (in watts)
- \( F \) = force (in newtons)
- \( v \) = velocity (in m/s)

### Step 4: Substitute Values into the Power Formula
Now we can substitute the values we have:
\[ P = 735 \, \text{N} \cdot 0.33 \, \text{m/s} \]

### Step 5: Calculate the Power
Now, we perform the multiplication:
\[ P = 735 \cdot 0.33 \]
\[ P = 242.55 \, \text{W} \]

### Conclusion
The power needed to lift the 75 kg student vertically upward at a constant speed of 0.33 m/s is approximately:
\[ P \approx 242.5 \, \text{W} \]