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?
To determine the change in thermal energy, we need to calculate the gravitational potential energy at the top of the slide and the kinetic energy at the bottom of the slide.
Step 1: Calculate the gravitational potential energy (GPE) at the top of the slide.
GPE = m * g * h
m = mass of the child = 17 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height of the slide = 2.7 m
GPE = 17 kg * 9.8 m/s^2 * 2.7 m
GPE = 448.2 J
Step 2: Calculate the kinetic energy (KE) at the bottom of the slide.
KE = 0.5 * m * v^2
m = mass of the child = 17 kg
v = speed at the bottom = 1.8 m/s
KE = 0.5 * 17 kg * (1.8 m/s)^2
KE = 0.5 * 17 kg * 3.24 m^2/s^2
KE = 27.72 J
Step 3: Calculate the change in thermal energy.
Change in thermal energy = KE - GPE
Change in thermal energy = 27.72 J - 448.2 J
Change in thermal energy = -420.48 J
The change in thermal energy of the slide and the seat of her pants is -420.48 J.
To find the change in thermal energy of the slide and the seat of her pants, we first need to calculate the gravitational potential energy at the top of the slide and the kinetic energy at the bottom of the slide. The change in thermal energy can be determined by subtracting the final energy from the initial energy.
1. Calculate the gravitational potential energy at the top of the slide:
Gravitational potential energy (GPE) is given by the formula GPE = mgh, where
m = mass (17 kg)
g = acceleration due to gravity (9.8 m/s²)
h = height (2.7 m)
GPE = 17 kg * 9.8 m/s² * 2.7 m
GPE = 457.14 Joules
2. Calculate the kinetic energy at the bottom of the slide:
Kinetic energy (KE) is given by the formula KE = (1/2)mv², where
m = mass (17 kg)
v = velocity (1.8 m/s)
KE = 0.5 * 17 kg * (1.8 m/s)²
KE = 54.54 Joules
3. Calculate the change in thermal energy:
Change in thermal energy = KE - GPE
Change in thermal energy = 54.54 Joules - 457.14 Joules
Change in thermal energy = -402.6 Joules (negative because energy is lost as heat)
Therefore, the change in thermal energy of the slide and the seat of her pants is -402.6 Joules.