A lift can hold 2000kg, friction is 4000N and power provided is 60HP. (1 HP = 746W) Find the maximum speed with which lift can move up.

Options

A. 1.9m/s
B. 1.7m/s
C. 2m/s
D. 1.5m/s

Answer

To solve the problem of finding the maximum speed with which the lift can move up, we will follow these steps:

### Step 1: Understand the Forces Acting on the Lift
The forces acting on the lift include:
- The weight of the lift (W) acting downwards.
- The friction force (f) acting downwards.
- The force (F) exerted by the lift's motor acting upwards.

The weight of the lift can be calculated using the formula:
\[ W = m \cdot g \]
where:
- \( m = 2000 \, \text{kg} \) (mass of the lift)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

### Step 2: Calculate the Weight of the Lift
Calculating the weight:
\[ W = 2000 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 20000 \, \text{N} \]

### Step 3: Calculate the Total Force Required to Move the Lift Up
The total force (F) required to lift the lift upwards against gravity and friction can be calculated as:
\[ F = f + W \]
where:
- \( f = 4000 \, \text{N} \) (friction force)

Calculating the total force:
\[ F = 4000 \, \text{N} + 20000 \, \text{N} = 24000 \, \text{N} \]

### Step 4: Convert Power from Horsepower to Watts
The power provided to the lift is given as 60 HP. We need to convert this to watts:
\[ \text{Power (P)} = 60 \, \text{HP} \times 746 \, \text{W/HP} = 44760 \, \text{W} \]

### Step 5: Use the Power Formula to Find Maximum Speed
The power can also be expressed in terms of force and velocity:
\[ P = F \cdot V \]
From this, we can solve for the maximum speed (V):
\[ V = \frac{P}{F} \]

### Step 6: Substitute the Values to Find Maximum Speed
Substituting the values we have:
\[ V = \frac{44760 \, \text{W}}{24000 \, \text{N}} \]

Calculating the maximum speed:
\[ V = 1.865 \, \text{m/s} \]

### Step 7: Round Off the Result
Rounding off the result to one decimal place gives:
\[ V \approx 1.9 \, \text{m/s} \]

### Final Answer
The maximum speed with which the lift can move up is approximately **1.9 m/s**.

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