Arunner goes from moving with a kinetic energy of 150 J to a complete stop in 5 seconds. How much power did the runner generate?

(a) 0.1134 L

(b) 2.009 L

(c) 0.07 cm from the top

Explanation:

The volume of the aluminum container and the turpentine is 2.000 L at  23 °C.

(a) When the entire system is heated to from 23 °C to 91 °C. The volume of the aluminum container is:

Vf = Vi*(1 + 3α*ΔT)

where:

Vi is the initial volume, Vf the final volume, α is the linear expansion coefficient and ΔT is the temperature change.

Vf = 2*[1 + 3*2.4 *10^-5*(91 - 23)] = 2.009 L

The volume of the turpentine is

Vf = Vi*(1 + β*ΔT)

where:

β is the  volume expansion coefficient

Vf = 2*[1 + 9.0*10^-4*(91 - 23)] = 2.1224 L

The overflow is:

2.1224  - 2.009 = 0.1134 L

(b) the volume of turpentine remaining in the cylinder at 91 °C is the same volume of the hollow aluminum cylinder, that is, 2.009 L

(c) Cooling the system back to 23 °C means the aluminum container is back to 2.000 L. The  volume of turpentine is:

Vf = 2.1224*[1 + 9.0*10^-4*(23-91)] = 1.9925 L

The following proportion must be  satisfied:

Volume of turpentine / Volume of container = deep turpentine / deep of container

1.9925 / 2.000 = deep turpentine/19

deep turpentine = (1.9925 / 2.000)*19 = 18.93 cm

This is 19 - 18.93 = 0.07 cm from the top