Homework 5 Solutions

Physics 101

One Steps:
7-2:  W = F * d = 20 N * 3.5 m = 70 J

7-4: The work done is W = F*d = 1 N * 2 m = 2 J
The power P = W/t = 2 J / 1 s = 2 W
(Do not confuse the W that is the symbol for work with the W that is
the abbreviation for the unit Watt.)

7-10:  KE = (1/2)mv2 = 0.5 * 1 kg * (2 m/s)2 = 2 kg-m2/s2 = 2 J

Exercises:
7-4: There are two ways to solve this a) symbolically and b) numerically.  Here's the symbolic method first:
Your work Wy = Fy * dy
Friend's work Wf = Ff * df = (0.5 * Fy) * (4 * dy) = 2 * Wy 

Here's the numeric method:
Arbitrarily choose that you apply 1 N of force over a distance of 1 m
Then Wy = 1 N * 1 m = 1 J
and Wf = 0.5 N * 4 m = 2 J

Either way, your friend does twice the work you do.

7-16: A baseball has more mass than a golf ball.  If they have the same momentum, then you have
mv = mv so that  the baseball has a slower speed than the golf ball. Kinetic energy = KE = (1/2)mv2 or KE = (1/2)p*v.  Since both balls have the same momentum, but the baseball has a slower speed, the baseball will have less KE.

7-24: Forces only do work when the direction of motion is at least partially in the direction of the force.  If the motion is perpendicular to the force, then the force does zero work.  The bowling alley is absolutely horizontal, therefore the force of gravity is perpendicular to the motion of the bowling ball and gravity does no work.

For the satellite in circular orbit, at any instant its velocity is tangent to its orbit and the gravitational force on it is radially inward (see figure).  The force and motion are thus perpendicular.
figure of satellite orbit

7-26: The string supporting the pendulum bob does zero work.  Since the string is always the same length, the bob always moves perpendicular to the string.  The force exerted by the string is always along the string and is therefore always perpendicular to the bob's motion.

The force of gravity does do work on the bob since the motion of the bob has a vertical component (ie: it's vertical position changes).

7-28: Thermal energy is involved (as you may remember from sliding too fast on a loooong slide).  100 J are converted to thermal energy.

7-38: When you open the windows, there is more air resistance to the motion of the car.  This effect gets larger at faster speeds.

7-44: The net force is zero for a car travelling at constant velocity.  Similarly, the net work done on the car is zero.  However, there are many forces acting on the car.  The force of the engine (transmitted to the ground via the wheels) does positive work and the forces of friction and air resistance do negative work.

7-50: Yes, you can have energy without momentum.  There are two ways to do this: 1) an object can have potential energy and zero velocity, or 2) a system can be composed of two objects that have equal and opposite momenta so that the system has zero momentum but it has energy. 
No, you cannot have momentum without energy.  If you have momentum, you have mass and velocity and therefore you have kinetic energy.

Note to the grader: sophisticated arguments about a negative potential energy cancelling a positive kinetic energy are also acceptable.  Use your judgment.

Problems:
7-4: The car starts with a certain amount of kinetic energy.  This is reduced to zero by the brakes doing negative work on the car.  Therefore, KE + W = 0 or KE + F*(-d) = 0 or  d = KE / F.  We assume that the road applies the same force to the locked wheels, regardless of speed. 

Since KE = (1/2)mv2 , when you triple the velocity, the KE increases by a factor of 32 = 9.  Therefore, your stopping distance increases by a factor of 9 from 15 m to 135 m.  Ouch!

7-6: Look figure 7.17.  Fd = Fd.  Thus,
5000 N * 0.2 m = F * 2 m (where F is the force the workers apply).  Thus
F = 5000 N * 0.2 m / 2 m = 500 N (or about 100 lbs)

Estimation:

From last time, we have the mass of a drifting continent m = 3*1021 kg and the speed of the continent v = 2*10-9 m/s so that the kinetic energy is KE = (1/2)mv2  = (1/2) * 3*1021 kg * (2*10-9 m/s)2 = 6*103 J.  That's not too large.

A fastball can travel at 100 mph ~ 50 m/s (since 2 mph is approximately 1 m/s).   The mass of a baseball is a lot more than an ounce and a bit less than a pound so I'll estimate it at about 1/4 pound.  Since 2.2 lb = 1 kg, 1/4 lb ~ 1/8 kg = 120 g.  You can google it and get that it is exactly 5 1/8 ounces or  142 g.  This means that the kinetic energy of a baseball is
KE = (1/2) * (0.1 kg) * (50 m/s)2 =  1*102 J.
Wow!  100 fastballs have more kinetic energy than a drifting continent!

Now let's look at the truck.  The mass of an 18-wheeler is about 40 tons = 4*103 kg.  The speed is 65 mph ~ 30 m/s.  Therefore:
KE = (1/2) * 4*103 kg * (30 m/s)2 = 2*106 J.
This is a LOT more than a drifting continent!

Larry Weinstein
Last modified: Tue Oct 11 10:42:06 EDT 2005