1. Last Time:
Dynamics: Forces
Newton’s Laws of Motion, Gravitation, Weight
Today:
Applications of Newton’s Laws of Motion
 Free Body Diagrams
HW #3 due Tuesday, Sept 21, 11:59 p.m.
(Last HW before Exam #1)
Exam #1 on Thursday, Sept 23
Formula sheet will be posted by Monday night

2. section of rope with mass m
Tension in a Rope
The tension in a rope is the magnitude of the force exerted along the rope.
section of rope with mass m x T T’
Neglecting friction and the mass of the rope (m = 0):
The tension is the SAME at all points along the rope.

3. Free-Body Diagram n sled T Fg
If we want to analyze the motion of an object subject to forces, we must identify ALL of the forces acting on it.
A “free-body diagram” is used to identify all of the forces that would act on an otherwise free body.
Suppose dogs/sled moving in x-direction
Assuming friction is negligible … n
sled y T x Fg

4. Free-Body Diagram n sled T Fgx y
Important point: Only the “action forces” are included in the free-body diagram. The reaction forces:
Force exerted by rope on dog
Gravitational force exerted by sled on the Earth
Force exerted by the sled on the ground
all act on different objects (NOT on the sled!).

5. Free-Body Diagram n sled T Fg x-direction : y-direction :
(constant)
If sled starts from rest :

6. Objects in Equilibrium
Key Point :
Objects that are either at rest, or moving with constant velocity, are said to be in equilibrium. These objects have an acceleration of a = 0.
Recall Newton’s Second Law :
Since the acceleration a = 0 for an object in equilibrium :
The sum of the x-components of all the forces is 0.
The sum of the y-components of all the forces is 0.

7. Example 4.5 (p. 96)
A traffic light weighing 100 N hangs from a vertical cable tied to two other cables, that are fastened to supports. Find the tension in each of the three cables.

8. Example 4.5 (p. 96)
A traffic light weighing 100 N hangs from a vertical cable tied to two other cables, that are fastened to supports. Find the tension in each of the three cables.

9. Example
An object with mass m slides down an inclined plane with an angle of θ. Assuming the plane is frictionless, what is the object’s acceleration? What is the magnitude of the normal ? θ

10. Example
An object with mass m slides down an inclined plane with an angle of θ. Assuming the plane is frictionless, what is the object’s acceleration? What is the magnitude of the normal ? y n x
mg cosθ θ θ
mg sinθ mg

11. Example: 4.28
Two crates are connected by a light string that passes over a frictionless pulley. Find the acceleration of the 5 kg crate and the tension in the string.

12. Example: 4.28 x y T n θ mg
mg cosθ
mg sinθ
5.0 kg T
10.0 kg mg

13. “Atwood’s Machine”
Two objects with m2 > m1 are connected by a light, inextensible cord, and hung over a frictionless pulley. The cord and pulley have negligible mass.
Find the magnitude of the acceleration of the system and the tension.

14. “Atwood’s Machine”

15. Example: 4.33
An 80-kg stuntman jumps from a window of a building situated 30 m above a catching net.
Assuming air resistance exerts a 100-N force on him as he falls, determine his velocity just before he hits the net.

16. Reading Assignment
Next class: 4.6
Friction