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 1