University Physics: Mechanics Ch5. Newton’s Laws of Motion Lecture 8 Dr.-Ing. Erwin Sitompul

8/2 Erwin SitompulUniversity Physics: Mechanics Homework 6: Two Boxes and A Pulley A block of mass m 1 = 3.7 kg on a frictionless plane inclined at angle θ = 30° is connected by a cord over a massless, frictionless pulley to a second block of mass m 2 = 2.3 kg. What are: (a) the magnitude of the acceleration of each block, (b) the direction of the acceleration of the hanging block, and (c) the tension in the cord?

8/3 Erwin SitompulUniversity Physics: Mechanics a Solution of Homework 6 T T m1gm1g m2gm2g a m 1 gcosθ m 1 gsinθ FNFN Forces on m 1 along the x axis: Forces on m 2 along the y axis: What is the meaning of negative sign?

8/4 Erwin SitompulUniversity Physics: Mechanics Solution of Homework 6 (a) The magnitude of the acceleration of each block (b) The direction of the acceleration of the hanging block (c) The tension in the cord Down Assumption: The acceleration points upward Result: Negative value Conclusion: The true acceleration points downward

8/5 Erwin SitompulUniversity Physics: Mechanics A passenger of mass kg stands on a platform scale in an elevator cab. We are concerned with the scale reading when the cab is stationary and when it is moving up or down. (a)Find a general solution for the scale reading, whatever the vertical motion of the cab. (b) What does the scale read if the cab is stationary or moving upward at a constant 0.5 m/s? (c)What does the scale read if the cab acceleration upward 3.2 m/s 2 and downward at 3.2 m/s 2 ? Applying Newton’s Law: Problem 3

8/6 Erwin SitompulUniversity Physics: Mechanics (a)Find a general solution for the scale reading, whatever the vertical motion of the cab. The scale reading is equal to F N, which is the force exerted by the surface of the scale towards the passenger → (b)What does the scale read if the cab is stationary or moving upward at a constant 0.5 m/s? In stationary condition or when moving upward with a constant velocity, the acceleration of passenger is zero Applying Newton’s Law: Problem 3

8/7 Erwin SitompulUniversity Physics: Mechanics (c)What does the scale read if the cab acceleration upward 3.2 m/s 2 and downward at 3.2 m/s 2 ? If the cab accelerates upward, the magnitude of acceleration is positive It the cab accelerates downward, the magnitude of acceleration is negative Applying Newton’s Law: Problem 3

8/8 Erwin SitompulUniversity Physics: Mechanics What does the scale read if, in case accident happens, the cab falls vertically downward? Applying Newton’s Law: Problem 3 a = –g

8/9 Erwin SitompulUniversity Physics: Mechanics The figure below shows two blocks connected by a cord (of negligible mass) that passes over a frictionless pulley (also of negligible mass). One block has mass m 1 = 2.8 kg; the other has mass m 2 = 1.3 kg. Determine: (a) the magnitude of the blocks’ acceleration. (b) the tension in the cord. Applying Newton’s Law: Problem 4 Atwood Machine

8/10 Erwin SitompulUniversity Physics: Mechanics T T m1gm1g m2gm2g a a Mass m 1 Mass m 2  The acceleration of m 1 and m 2 have the same magnitude a, oppose in direction.  We take the acceleration of m 1 as negative (downward) and of m 2 as positive (upward). Applying Newton’s Law: Problem 4

8/11 Erwin SitompulUniversity Physics: Mechanics Applying Newton’s Law: Problem 4 (a) The magnitude of the blocks’ acceleration (b) The tension in the cord What happen if m 2 > m 1 ?

8/12 Erwin SitompulUniversity Physics: Mechanics Virtual Experiment: Atwood Machine Two masses of 550 g and 560 g are connected through a pulley to construct an Atwood machine. If the masses are released from rest, how much time is required for the masses to move a distance of 1 m?

8/13 Erwin SitompulUniversity Physics: Mechanics Example: Particle Movement A 2 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by x = 3 m + (4 m/s)t + ct 2 – (2 m/s 3 )t 3, with x in meters and t in seconds. The factor c is a constant. At t = 3 s, the force on the particle has a magnitude of 36 N and is in the negative direction of the axis. What is c?

8/14 Erwin SitompulUniversity Physics: Mechanics Hanging Chair A man sits in a chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man’s hand. The combined mass of man and chair is 95 kg. With what force magnitude must the man pull on the rope if he is to rise (a) with a constant velocity and (b) with an upward acceleration of 1.3 m/s 2 ? (a) (b) TATA F g = mg TATA a TBTB TBTB

8/15 Erwin SitompulUniversity Physics: Mechanics Hanging Chair Continuing the same problem, if the rope on the right extends to the ground and is pulled by a co- worker, with what force magnitude must the co- worker pull for the main to rise (c) with a constant velocity and (d) with an upward acceleration of 1.3 m/s 2 ? (c) (d) F g = mg TCTC a TBTB What is the magnitude of the force on the ceiling from the pulley system in each of 4 cases?

8/16 Erwin SitompulUniversity Physics: Mechanics A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in the figure below. The upper cables make angles of 37° and 53° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100N. Will the traffic light remain hanging in this situation, or will one of the cables break? Homework 7: The Traffic Light

8/17 Erwin SitompulUniversity Physics: Mechanics Homework 7A 1.Two forces are applied to a ring that is lying on a frictionless surface. It is shown on the figure from the bird’s-eye-view. If the mass of the ring is 6 kg, determine the position of the ring 2 seconds after the two forces are applied. 2.Joe’s Advertising wishes to hang a sign weighing N so that cable A, attached to the store makes a 30.0° angle, as shown in the figure. Cable B is horizontal and attached to and adjoining building. What is the tension in cable B?

8/18 Erwin SitompulUniversity Physics: Mechanics θ Homework 7B 1.As your jet plane speeds down the runway on takeoff, you decide to determine its acceleration, so you take out your yo-yo and note that when you suspend it, the string makes an angle of 22° with the vertical (see figure). (a) What is the acceleration of the plane? (b) If the mass of the yo-yo is 40 g, what is the tension in the string? Hint: Decompose the tension T. 2.In the next figure, let the mass of the block be 8.5 kg and the angle θ be 30°. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the elevation decrease of the mass after moving for 0.8 s (assuming it does not reach the floor). a