A crane pulls up a car of mass 500kg to a vertical height of 4m. Calculate the work done by the crane.

Explanation

To calculate the work done by the crane in lifting the car, we can use the formula for work done against gravity:

\[ \text{Work Done} (W) = \text{Force} (F) \times \text{Distance} (d) \]

### Step 1: Identify the Force
The force exerted by the crane to lift the car is equal to the weight of the car. The weight (force due to gravity) can be calculated using the formula:

\[ F = m \times g \]

Where:
- \( m = 500 \, \text{kg} \) (mass of the car)
- \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity)

### Step 2: Calculate the Weight of the Car
Substituting the values into the formula:

\[ F = 500 \, \text{kg} \times 9.81 \, \text{m/s}^2 \]
\[ F = 4905 \, \text{N} \]

### Step 3: Identify the Distance
The distance the car is lifted is given as:

\[ d = 4 \, \text{m} \]

### Step 4: Calculate the Work Done
Now, we can calculate the work done by the crane:

\[ W = F \times d \]
\[ W = 4905 \, \text{N} \times 4 \, \text{m} \]
\[ W = 19620 \, \text{J} \]

### Final Answer
The work done by the crane in lifting the car is:

\[ W = 19620 \, \text{Joules} \]

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