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?
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To find the change in thermal energy, we need to determine the change in her gravitational potential energy and her kinetic energy.
First, let's find the change in gravitational potential energy (ΔPE). We can use the formula:
ΔPE = mgh
where m is the mass (17 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slide (2.7 m):
ΔPE = (17 kg)(9.8 m/s^2)(2.7 m)
ΔPE = 444.26 J
Next, let's find the change in kinetic energy (ΔKE). We can use the formula:
ΔKE = 1/2 mv^2
where m is the mass and v is the velocity (1.8 m/s):
ΔKE = (1/2)(17 kg)(1.8 m/s)^2
ΔKE = 55.08 J
Now, to find the change in thermal energy, we sum the change in gravitational potential energy and the change in kinetic energy:
Δthermal energy = ΔPE + ΔKE
Δthermal energy = 444.26 J + 55.08 J
Δthermal energy = 499.34 J
Therefore, the change in thermal energy of the slide and the seat of her pants is approximately 499.34 Joules.