A 24 kg child descends a 5.0 m high slide and reaches the ground with a speed of 2.8 m/s.
a. How much energy was dissipated due to friction in the process?
Would it be 1081.92 J
initial PE = mgh
final KE = 1/2 mv^2
subtract to find energy loss due to friction
To calculate the energy dissipated due to friction, we will use the conservation of energy principle. The initial potential energy of the child at the top of the slide will be equal to the final kinetic energy at the bottom of the slide plus the energy dissipated due to friction.
The potential energy of the child at the top of the slide can be calculated using the formula:
Potential energy = mass × gravitational acceleration × height
Potential energy = 24 kg × 9.8 m/s^2 × 5.0 m
Potential energy = 1176 J
The kinetic energy of the child at the bottom of the slide can be calculated using the formula:
Kinetic energy = 1/2 × mass × velocity^2
Kinetic energy = 1/2 × 24 kg × (2.8 m/s)^2
Kinetic energy = 94.08 J
Now, we can calculate the energy dissipated due to friction:
Energy dissipated = Potential energy - Kinetic energy
Energy dissipated = 1176 J - 94.08 J
Energy dissipated ≈ 1081.92 J
Therefore, the energy dissipated due to friction in the process is approximately 1081.92 J.
To determine the amount of energy dissipated due to friction, we need to first calculate the potential energy the child had at the top of the slide using the formula:
Potential energy (PE) = mass (m) × gravitational acceleration (g) × height (h)
Given:
mass (m) = 24 kg
gravitational acceleration (g) = 9.8 m/s²
height (h) = 5.0 m
PE = 24 kg × 9.8 m/s² × 5.0 m
PE = 1176 J (Joules)
Next, we need to calculate the kinetic energy the child had when reaching the ground using the formula:
Kinetic energy (KE) = 0.5 × mass (m) × velocity² (v)
Given:
mass (m) = 24 kg
velocity (v) = 2.8 m/s
KE = 0.5 × 24 kg × (2.8 m/s)²
KE = 94.08 J (Joules)
The difference between the initial potential energy (PE) and the final kinetic energy (KE) represents the amount of energy dissipated due to friction:
Energy dissipated = PE - KE
Energy dissipated = 1176 J - 94.08 J
Energy dissipated = 1081.92 J (Joules)
Therefore, approximately 1081.92 Joules of energy were dissipated due to friction in the process.