Homework Ch. 7 Work and Energy - Due W 3/21 in class. PHY 161 General Physics I: Mechanics and Thermodynamics Physics Department --- Mercer University --- Spring 2007 PLEASE NOTE: The instructor’s preference is that your homework solutions be handwritten on printed copies of these pages and/or blank standard printer paper sheets (8 ½” x 11”), front and back... But if absolutely necessary, you may use notebook pages; in that case, please remove the paper fringes. 1. (NOTE UNITS) A boat experiences a frictional force directed opposite its velocity, whose magnitude is given by f = Cv, where C is an unknown constant. If the boat’s motor supplies 200 hp of power, the boat moves at a constant speed of 67.2 mi/h (miles per hour). a) What is the constant C, in SI units? b) If the boat’s new motor supplies 250 hp, what is the boat’s new constant speed, in mi/h? 2. A truck stands at rest with a cargo box on its bed; there is substantial friction between the cargo bed and box. The truck mass is 3000 kg; the box mass is 300 kg. The truck engine applies a constant force F to the truck, so that the truck and box accelerate through a 100 m straight track. It takes the truck 6.26 s to cover the distance. At that time, the box is seen to have slipped backward by 3.92 m relative to the truck; it was sliding against the cargo bed the entire time… (Note: A constant force F is not very realistic, but this makes the problem much easier than the more physical alternatives, either constant power with varying force or even varying force and power.) a) What is the coefficient of kinetic friction μκ between cargo bed and box? b) Use the Work-Energy Theorem (not kinematics) to find the final speed of the box. c) Use the Work-Energy Theorem (not kinematics) to find the final speed of the truck. 3. A block with mass of 3 kg is released 4 m from an ideal (massless) spring with a force constant of 120 N/m that is fixed along a frictionless plane inclined at 30° as shown below. a) Find the maximum compression of the spring. b) If the plane is not frictionless and the coefficient of kinetic friction is μκ = 0.2, find the maximum compression. c) For the incline with friction, how far up the incline will the block travel after leaving the spring? 4. A pendulum is constructed from a thin massless rod of length L = 50 cm and a bob with mass m = 250 g. The angle θ measures the angle from the bottom as shown. a) The bob is released at the bottom (θ = 0°) with speed v0. What must v0 be so the rod will have zero tension at the top (θ = 90°)? b) Under these conditions, what is the power exerted by gravity on the bob when θ = 0°, 30°, 45°, 90° and 135°?