Lecture 9 Serway and Jewett : 5.7, 5.8 Newton’s Laws applied to systems with two or more accelerated bodies. Serway and Jewett : 5.7, 5.8 Physics 1D03 - Lecture 9

Problems with several accelerated objects: Free-body diagram for each object. Relate forces by finding action-reaction pairs, etc. Look for constraints on the motion to relate accelerations. “F=ma” for each diagram, break into components. Count unknowns: do you have enough equations? Use algebra to solve. Physics 1D03 - Lecture 9

Two blocks connected by a rope are being pulled by a horizontal force FA. Given that F=60 N, m1=12kg and m2=18kg, and that μk=0.1, find the tension in the rope between them and the acceleration of the system. T m2 FA m1 Physics 1D03 - Lecture 9

Atwood’s Machine Assume : - no friction Calculate the acceleration of the blocks. Assume : - no friction - massless rope and pulley - rope doesn’t stretch Plan: • free-body diagram for each mass • relate tensions, accelerations • use Newton’s second Law m1 m2 Physics 1D03 - Lecture 9

Constraints on the motion: Why are the accelerations equal (in magnitude)? Because the cord doesn’t stretch! Any downward motion of m1 requires an equal upward motion of m2. This is a constraint on the motion, which comes from the geometry of the apparatus. Label directions of a consistently on both diagrams: if m1 accelerates up, m2 accelerates down. Physics 1D03 - Lecture 9

T1 T2 a2 a1 m2g m1g Forces on m1 Forces on m2 Tensions are equal (“ideal” pulley, light rope) Accelerations are equal in magnitude (why?), opposite in direction Physics 1D03 - Lecture 9

is proportional to g, but can be small (and easy to measure) m2g a m1g . Eliminate T to get  is proportional to g, but can be small (and easy to measure) Physics 1D03 - Lecture 9

m2 m1 a1 Concept Quiz Consider the more elaborate Atwood’s machine shown. Assuming the rope and pulleys are ideal, the relation between the accelerations will be: a2 Physics 1D03 - Lecture 9

A block of mass m1 on a rough horizontal surface is pulled with a force FA at an angle θ to the horizontal. A ball of mass m2 is connected to the other side, hanging over a lightweight frictionless pulley. The coefficient of friction is given by μk. Determine the acceleration of the system. FA θ m1 m2 Physics 1D03 - Lecture 9

Eg: Given no friction, determine the acceleration of the system and the tension in the strings. Physics 1D03 - Lecture 9

m FP M Example: How do you calculate the acceleration of each block: if the upper block doesn’t slide? if the upper block does slide? m = 1.0 kg M = 2.0 kg ms = 0.6 mk = 0.4 FP = 15 N m FP M Physics 1D03 - Lecture 9

Suggested Problems Chapter 5: Problems 17, 25, 29, 43, 44, 62, Questions 19, 21 Physics 1D03 - Lecture 9