The potential energy, E, of the penny is given by E=mgh. The energy, Q, required to raise the temperature of an object by an amount ΔT is given by Q=mcΔT. We can equate these two to get the result but we must use proper units and include the 60%:
(0.6)mgh=mcΔT
We see we can divide out the mass from each side
0.6gh=cΔT, then 0.6gh/c=ΔT
(0.6)9.81(m/s²)50m/385(J/kg°C) = 0.7644°C
since this is the change in temperature and it started at 25°C we get
T=25.7644°C
As you can see the result does not depend on mass. The more massive the copper object the more potential energy it will have to contribute to the heat energy, but the more stuff there will be to heat up, and the effect is that the mass cancels.
The answer to your question is $231
3,000 yd3 = 200 dtl
Chapter 1: Problem Solving 17 / 21
Rates Question
12 A highway had a landslide, where 3,000 cubic yards of material fell on the road, requiring 200 dump truck loads to clear. On another highway, a slide left 40,000 cubic yards on the road. How many dump truck loads would be needed to clear this slide?
3,000 yd3 = 200 dtl
40,000 yd3 × 200 dtl = 2,667 dtl
3, 000 yd3
The fact that the first chosen student was a girl is already decided, so there is no need to find the probability of that happening. There are a total of 13+10, or 23 students. A girl was already selected, so that leaves 22 students. The chance that a boy is chosen is 10/22, or 5/11.
