A 17kg child slides down a 2.7m -high playground slide. She starts from rest, and her speed at the bottom is 1.8 m/s. What is the change in the thermal energy of the slide and the seat of her pants?
U =mgh-mv²/2
To calculate the change in thermal energy of the slide and the seat of her pants, we need to know the amount of heat transferred between them.
The change in thermal energy can be calculated using the equation:
ΔQ = m × c × ΔT
Where:
ΔQ is the change in thermal energy
m is the mass
c is the specific heat capacity
ΔT is the change in temperature
First, let's find the change in temperature. Since the child starts from rest, we can assume that the initial kinetic energy is converted entirely into thermal energy at the bottom.
The kinetic energy of the child at the bottom of the slide can be calculated using the equation:
KE = 1/2 × m × v²
Where:
KE is the kinetic energy
m is the mass
v is the velocity
Next, we can find the change in thermal energy using the equation:
ΔQ = KE
Now, let's calculate the change in thermal energy:
1. Calculate the kinetic energy:
KE = 1/2 × 17 kg × (1.8 m/s)²
KE = 1/2 × 17 kg × 3.24 m²/s²
KE = 27.72 J
2. Calculate the change in thermal energy:
ΔQ = 27.72 J
Therefore, the change in thermal energy of the slide and the seat of her pants is 27.72 Joules.