UNIVERSITY OF CAPE TOWN DEPARTMENT OF PHYSICS PHY1010W − 2008 Weekly Problem Set 6 Hand in your solutions in the box corresponding to the first letter of your last name (surname) outside the Physics I Laboratory before 14h00 on Thursday 10 April. The solutions must be your own work. Questions 1, 2 and 3 are taken from Test 2 of 2007. r ˆ j 1. A 2.00 kg object is subjected to three forces that give it an acceleration a = − 8.00 m/s 2 i + 6.00 m/s 2 ˆ. If r ˆ two of the three forces are F1 = (30.0 N ) i + (16.0 N ) ˆ and j r F2 = − (12.0 N ) iˆ + (8.0 N ) ˆ, find the third force. j 2. A 2.0 kg book is pressed against a wall as shown. If the coefficient of static friction for the book and the wall is 0.30, calculate the minimum horizontal force required to prevent the book from slipping. ( ) ( ) 3. A 500 g model rocket is resting horizontally at the top edge of a 40 m high wall when it is accidentally bumped. The bump pushes it off the edge with a horizontal speed of 0.5 m/s and at the same time causes the engine to ignite. When the engine fires, it exerts a constant 20 N horizontal thrust away from the wall. (a) How far from the base of the wall does the rocket land? (b) If the rocket is not bumped, but intentionally ignited by the experimenter, its initial horizontal speed will be zero. Describe the trajectory of the rocket while it travels to the ground. Explain you reasoning clearly using equations of motion where necessary. 4. A large crate is suspended from the end of a vertical rope. Is the tension in the rope larger when the crate is at rest or when it is moving upward at constant speed? If the crate is travelling upward, is the tension in the rope greatest when the crate is speeding up or when it is slowing down? In each case explain in terms of Newton’s laws of motion. 5. A worker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00 s. (a) What is the mass of the block of ice? (b) If the worker stops pushing at the end of 5.00 s, how far does the block move in the next 5.00 s? 6. A man is dragging a trunk up a loading ramp of a mover’s truck. The ramp has a slope angle of 20.0º, and the man pulls upward with r a force F whose direction makes an angle of 30.0° with the ramp (see figure). r (a) How large a force F is necessary for the component Fx parallel to the ramp to be 60.0 N? (b) How large will the component Fy perpendicular to the ramp then be? (c) If the 7,8 kg trunk starts from rest at the bottom of the 3 m-long ramp, and the man pulls with the force calculated in (a), how long will it take to get the trunk into the truck, and at what speed will it enter the truck? Try the following problems from the textbook, Physics for Scientists and Engineers, by Randall D Knight. Seek help from the Class Tutor if you have any difficulties. Chapter 4: 30, 33, 40 and 46. Laboratory homework: Read and complete the exercises in chapter 4 of “Introduction to Measurement in the Physics Laboratory” before you go to the next Laboratory Tutorial session (07 April – 11 April).