An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy ? If the object is allowed to fall, find its kinetic energy when it is half - way down.

Explanation

To solve the problem step by step, we will first calculate the potential energy of the object when it is raised to a height of 5 meters, and then we will determine its kinetic energy when it is halfway down.

### Step 1: Calculate the Potential Energy (PE)

The formula for potential energy (PE) is given by:
\[ PE = mgh \]
where:
- \( m \) = mass of the object (in kg)
- \( g \) = acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \))
- \( h \) = height above the ground (in meters)

Given:
- \( m = 40 \, \text{kg} \)
- \( g = 10 \, \text{m/s}^2 \)
- \( h = 5 \, \text{m} \)

Substituting the values into the formula:
\[ PE = 40 \, \text{kg} \times 10 \, \text{m/s}^2 \times 5 \, \text{m} \]
\[ PE = 2000 \, \text{Joules} \]

### Step 2: Determine the Kinetic Energy (KE) when the object is halfway down

When the object is halfway down, it has fallen to a height of \( \frac{h}{2} = \frac{5}{2} = 2.5 \, \text{m} \).

#### Step 2.1: Calculate the Potential Energy at halfway down

Using the potential energy formula again:
\[ PE_{half} = mgh_{half} \]
where \( h_{half} = 2.5 \, \text{m} \):
\[ PE_{half} = 40 \, \text{kg} \times 10 \, \text{m/s}^2 \times 2.5 \, \text{m} \]
\[ PE_{half} = 1000 \, \text{Joules} \]

#### Step 2.2: Apply the Conservation of Energy Principle

According to the conservation of energy:
\[ \text{Initial Total Energy} = \text{Final Total Energy} \]
This can be expressed as:
\[ \text{Initial KE} + \text{Initial PE} = \text{Final KE} + \text{Final PE} \]
Initially, the object is at rest, so:
\[ \text{Initial KE} = 0 \]
Thus:
\[ 0 + 2000 \, \text{J} = KE_{final} + 1000 \, \text{J} \]

Rearranging gives:
\[ KE_{final} = 2000 \, \text{J} - 1000 \, \text{J} \]
\[ KE_{final} = 1000 \, \text{Joules} \]

### Final Answers:
1. The potential energy of the object when raised to a height of 5 m is **2000 Joules**.
2. The kinetic energy of the object when it is halfway down is **1000 Joules**.