Download Problem Set 5 - from Chapter 6 Exercises 2, 5, 7, 15, 18, 32

Problem Set 5 - from Chapter 6
Exercises 2, 5, 7, 15, 18, 32
Problems 1, 5, 8, 11
2. In order for you to get out of bed with the least amount of work, would it be better for
your bed to be on the floor or about a meter high? Explain.
It would be better if the bed were a meter high, because then you would not have to lift
yourself up. (Gravity does the work for you, so you do not have to act against it).
5. Which of the eight physical types of energy was the basis for the earliest human
culture? Which was the basis for the Industrial Revolution?
Chemical energy, in the form of food, was the basis for the earliest human culture.
Chemical energy, in the form of fossil fuels, was the basis for the Industrial Revolution.
7. Name the main type of energy possessed by each of the following:
a) Dynamite (chemical)
b) Water at rest behind a high dam (gravitational)
c) A bow about to release an arrow (elastic)
d) A wooden match (chemical)
e) Food (chemical)
15.
a) Where would an apple have greater gravitational energy, at 100 km high or at
1000 km high?
At 1000 km high.
b) Would the gravitational energy of an orbiting satellite be increased or
decreased by moving it from an orbit that is 6000 km high up to an orbit that is 12000 km
high?
The gravitational energy would be increased.
c) At which point, 6000 km high or 12000 km high, does a satellite have a larger
gravitational force on it?
The force at 6000 km high is greater than the force at 12000 km, even though the energy
at 12000 km high is greater than the energy at 6000 km.
18. Give an example in which chemical energy transforms into kinetic energy.
Some examples of this are: lighting a match, a bomb exploding, a car transforming
gasoline into the ability to move, a person’s body transforming food into the ability to
run.
1. Your left hand lifts a 2-N apple by 1.5 m, and your right hand lifts a 4-N grapefruit by
.5 m. Which hand did the most work?
Work = (Force)*(distance)
Work(of Left Hand) = (2N)*(1.5m) = 3 Nm
Work(of Right Hand) = (4N)*(.5m) = 2 Nm
3Nm>2Nm, therefore the left hand did the most work.
5. While driving down a highway you slam on the brakes, sliding a certain distance with
locked brakes. How much further would you slide if you had been moving twice as fast?
What if you had been moving half as fast?
1
Kinetic energy = mv 2 , where m is mass and v is velocity.
2
Since kinetic energy is dependent on the velocity squared, doubling the velocity of the
car (if you were moving twice as fast), means that the energy would increase by a factor
of 4. This means that work is increased by a factor of 4. W = Fd, and F (the force of
friction, in this case), is constant, so the distance increases by a factor of 4.
Similarly, if your speed were cut in half, the distance traveled would decrease by a factor
of four (you would only travel a fourth of the original distance).
8. Jack, who weighs 100 newtons, sits in a child’s swing. You pull the swing back so that
it is 2m above its low point, and release it. a) what form of energy, and how much
energy, does Jack have when he is pulled back and held at rest?
1
Kinetic energy = mv 2 , but v=0, so Kinetic energy =0
2
Potential energy = mgh, where mg is weight and h is height
Potential energy = (100N)(2m) = 200Nm
Total energy = Kinetic energy + Potential Energy = 0 + 200Nm = 200Nm
b) What form of energy, and how much energy, does Jack have as he swings through the
low point? (neglect air resistance and friction in the moving parts).
Because of the Law of Conservation of Energy, we know he still has an energy = 200Nm.
c) Still assuming no air resistance, how high should Jack be when he has swung forward
to his high point?
Because of the Law of Conservation of Energy, his energy at the forward high point is
200Nm. At that point, his velocity is zero (he is changing direction), and so kinetic
energy is zero.
Potential energy = 200Nm = mgh, as above. Jack’s weight, mg, is still 100N. Solve for
his height.
(200Nm)/100N = 2m. (The same height that he was at his initial high point!)