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 find 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, and then find the difference.
1. Calculate the gravitational potential energy at the top of the slide:
The gravitational potential energy (PE) is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
PE = 17 kg * 9.8 m/s^2 * 2.7 m
= 441.18 J
2. Calculate the kinetic energy at the bottom of the slide:
The kinetic energy (KE) is given by the formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity.
KE = 0.5 * 17 kg * (1.8 m/s)^2
= 27.54 J
3. Calculate the change in thermal energy:
Change in thermal energy = Kinetic energy at the bottom - Gravitational potential energy at the top
Change in thermal energy = 27.54 J - 441.18 J
= -413.64 J
The change in thermal energy of the slide and the seat of her pants is -413.64 Joules. The negative sign indicates that thermal energy is lost in this process.