# Applied Mechanics: Numerical Practice ## Step 1: Calculate Momentum The momentum (\( p \)) of a body is given by: \[ p = m \times v \] where \( m = 40\, \text{kg} \) (mass), \( v = 12\, \text{m/s} \) (velocity). \[ p = 40 \times 12 = 480\, \text{kg m/s} \] **Explanation:** Momentum is the product of mass and velocity. Here, multiplying 40 kg by 12 m/s gives a momentum of \( 480\, \text{kg m/s} \). --- ## Step 2: Calculate Kinetic Energy The kinetic energy (\( KE \)) is given by: \[ KE = \frac{1}{2} m v^2 \] \[ KE = \frac{1}{2} \times 40 \times (12)^2 \] \[ KE = 20 \times 144 = 288\, \text{J} \] **Explanation:** Kinetic energy depends on both mass and the square of velocity. Here, the calculation results in \( 288\, \text{J} \) (joules). --- ## Final Answer - **Momentum:** \( 480\, \text{kg m/s} \) - **Kinetic Energy:** \( 288\, \text{J} \)

# Applied Mechanics: Numerical Practice In this task, we will calculate the momentum and kinetic energy of a body with a mass of 40 kg moving at a uniform velocity of 12 m/s. We will break down the solution into two steps. ## Step 1: Calculate Momentum To find the momentum (\( p \)) of the body, we use the formula: \[ p = m \times v \] where: - \( m = 40\, \text{kg} \) (mass of the body) - \( v = 12\, \text{m/s} \) (velocity of the body) Substituting the values into the formula: \[ p = 40 \times 12 \] Calculating this gives: \[ p = 480\, \text{kg m/s} \] **Explanation:** Momentum is defined as the product of mass and velocity. Here, we multiply the mass (40 kg) by the velocity (12 m/s), resulting in a momentum of \( 480\, \text{kg m/s} \). This indicates the quantity of motion the body possesses. --- ## Step 2: Calculate Kinetic Energy Next, we will calculate the kinetic energy (\( KE \)) using the formula: \[ KE = \frac{1}{2} m v^2 \] Substituting the values: \[ KE = \frac{1}{2} \times 40 \times (12)^2 \] Calculating \( (12)^2 \): \[ (12)^2 = 144 \] Now substituting this back into the kinetic energy equation: \[ KE = \frac{1}{2} \times 40 \times 144 \] Calculating further: \[ KE = 20 \times 144 = 288\, \text{J} \] **Explanation:** Kinetic energy quantifies the energy of motion and is dependent on both the mass of the body and the square of its velocity. In this case, the calculation results in \( 288\, \text{J} \) (joules), indicating the energy due to the motion of the body. --- ## Final Answer - **Momentum:** \( 480\, \text{kg m/s} \) - **Kinetic Energy:** \( 288\, \text{J} \)