A boy on a swing reaches a maximum height of 3.2 m and a minimum height of .55 m. What is the speed of the boy at the lowest point if the boy has a mass of 34 kg?
v(final)=?
To find the speed of the boy at the lowest point, we can use the principle of conservation of mechanical energy.
Step 1: Determine the potential energy at the highest point
At the highest point of the swing, all of the potential energy has been converted to kinetic energy and no potential energy remains. Thus, the potential energy at the highest point is zero.
Step 2: Determine the potential energy at the lowest point
At the lowest point of the swing, all of the potential energy is converted to kinetic energy. The potential energy can be calculated using the formula:
Potential Energy = mass * gravitational acceleration * height
Given:
Mass (m) = 34 kg
Gravitational acceleration (g) = 9.8 m/s² (approximate value)
Height (h) = 0.55 m
Potential Energy at the lowest point = mass * gravitational acceleration * height
Potential Energy = 34 kg * 9.8 m/s² * 0.55 m
Potential Energy = 182.93 J
Step 3: Determine the kinetic energy at the lowest point
The kinetic energy can be found using the formula:
Kinetic Energy = 1/2 * mass * velocity²
Since the potential energy at the lowest point is fully converted to kinetic energy, we can equate them:
Kinetic Energy = Potential Energy
1/2 * mass * velocity² = Potential Energy
Solve the equation for velocity:
velocity = sqrt((2 * Potential Energy) / mass)
velocity = sqrt((2 * 182.93 J) / 34 kg)
velocity = sqrt(10.7788)
velocity ≈ 3.28 m/s
Therefore, the speed of the boy at the lowest point is approximately 3.28 m/s.