1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

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

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

11. 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

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