### Assignment 6 - Carl Grossman

```Physics 3 - General Physics I
Homework Assignment 6
Due Wednesday, October 19
Carl Grossman
Office: SC L38
Chapter 9
Problem 1 - At the end of a delivery ramp, a skid pad exerts a constant force on a package
so that the package comes to rest in a distance d. The skid pad is changed so that the
distance it takes for the same package to stop is d/2. What happens to the length of time
it takes for the package to stop? Answer: tnew = told /2
Problem 2 - Two 1.0-kg blocks, one gray and one tan, sit on a horizontal x axis. The
gray block is at x = −4.0 m, and the tan one is at x = +4.0 m. A constant force of 1.0
N acts on the gray block in the positive x direction through a distance of 2.0 m. Taking
the two blocks as the system, calculate the following at the moment when the gray block is
at x = −2.0 m: (a) the work done by the force on the system, (b) the change in the total
energy of the system, (c) the velocity of the system’s center of mass, (d) the change in the
kinetic energy of the system’s center of mass, (e) the value of F ∆xcm , where F = 1.0 N
and ∆xcm is the displacement of the system’s center of mass as the gray block moves from
x = −4.0 m to x = −2.0 m.. (f) If the blocks collide totally inelastically, what is the total
energy of the system after the collision? Answers: (a) 2.0 J, (b) 2.0 J , (c) 1.0 m/s, (d) 1.0
J, (e) 1.0 J, (f) 1 J.
Problem 3 - A bullet of inertia m traveling at speed v is fired into a wooden block that
has inertia 4m and rests on a level surface. The bullet passes through the block and emerges
with at speed v/3, taking a negligible amount of the wood with it. The block moves to
the right but comes to rest after traveling a distance d. (a) What is the magnitude of the
frictional force between the block and surface while the block is moving? (b) What is the
ratio of the energy dissipated as the bullet passes through the block to the energy dissipated
by friction between the surface and the bottom face of the block? Answers: (a) mv 2 /18d,
(b) 7
Problem 4 - Spring B is stiffer than spring A (kB > kA ). Show which one has more
energy stored in it if you (a) compress both springs with the same force and (b) compress
both springs the same displacement from their equilibrium lengths? (Derive expressions for
the stored energies EA and EB in terms the same force F or the same displacement ∆x.)
Answers: (a) EA > EB , (b) EB > EA
Problem 5 - A 1000-kg car starting at the bottom of a 20-m hill at 5.0 m/s almost
comes to a complete stop as it crests the hill, barely making it over the top (Figure 9.15).
The power rating of the engine is 67 kW. (a) Assuming the engines delivery of power just
accounts for the change in the car’s potential and kinetic energies as it moves from the
bottom of the hill to the top, how long does it take the car to make it up the hill under
full power? (b) Explain why this is not a reasonable answer, what assumption or condition
might be false? Answers: (a) 2.7 s
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