A stone has a mass of 500g. How much energy must be imparted to the stone in order that it escapes form the earth?

Explanation

To determine the energy required for a stone with a mass of 500 g to escape from the Earth, we can follow these steps:

### Step 1: Convert the mass of the stone to kilograms
The mass of the stone is given as 500 g. To use standard units in our calculations, we need to convert this mass into kilograms.

\[ \text{Mass in kg} = \frac{500 \text{ g}}{1000} = 0.5 \text{ kg} \]

### Step 2: Understand escape velocity
Escape velocity is the minimum velocity an object must reach to break free from the gravitational pull of a celestial body without any further propulsion. For Earth, the escape velocity is approximately 11.2 km/s.

### Step 3: Convert escape velocity to meters per second
Since we need to work in SI units, we convert the escape velocity from kilometers per second to meters per second.

\[ \text{Escape velocity} = 11.2 \text{ km/s} = 11.2 \times 10^3 \text{ m/s} = 11200 \text{ m/s} \]

### Step 4: Calculate the kinetic energy required
The kinetic energy (KE) required to impart this escape velocity to the stone can be calculated using the formula:

\[ KE = \frac{1}{2} mv^2 \]

Substituting the values we have:

\[ KE = \frac{1}{2} \times 0.5 \text{ kg} \times (11200 \text{ m/s})^2 \]

Calculating \( (11200)^2 \):

\[ (11200)^2 = 125440000 \]

Now substituting back into the kinetic energy formula:

\[ KE = \frac{1}{2} \times 0.5 \times 125440000 \]
\[ KE = 0.25 \times 125440000 = 31360000 \text{ J} \]

### Step 5: Final answer
Thus, the energy that must be imparted to the stone in order for it to escape from the Earth is:

\[ KE = 3.136 \times 10^7 \text{ J} \quad \text{or} \quad 31.36 \text{ MJ} \]

### Summary
The energy required for the stone to escape from the Earth is approximately \( 3.14 \times 10^6 \) joules.

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