1. Thursday(10/29): Introduction to Chap. 9, Momentum and

Impulse. HW: Read pages 228-235 and solve prob. 58, 59, 61,

64, and 67 on page 251.

2. Friday(10/30): The Law of Conservation of Momentum.

HW: Read pages 236-245 and solve prob. 76, 80, 83, 84, and 85

on page 253.

3. Monday(11/02): Lab on Momentum. HW: Process lab

data and begin to write lab report (Due Monday).

4. Tuesday(11/03): Post-Lab Discussion and Problem-solving.

HW: Finish writing lab report (Due Wednesday).

5. Wednesday(11/04): Review I for Chapter 9 - Momentum.

HW: Complete Review Handout.

6. Thursday(11/05):TEST on Ch.9 - Momentum. HW: Go to

web-site for notes on Ch.10 - Work and Energy.

1. The momentum of an object is the product of the object's mass and

its velocity. We use lowercase p for momentum and this gives the

formula p = mv .

2. Since mass is a scalar and velocity is a vector, momentum is a vector

because the product of a scalar and a vector is a vector.

3. So, anything we have done with vectors previously can be done with

momentum. It can be broken into horizontal and vertical components,

and several momentum vectors can produce a single resultant.

4. The Pythagorean theorem and SOHCAHTOA are still used to solve

momentum problems.

5. The unit for momentum in MKS is the kg m/s , but when working in

CGS we use g cm/s.

6. The change in momentum, Δp , of an object is equal to the impulse

that acts that acts on it. This is known as the Impulse-Momentum

Relation. This relation can also be derived from Newton's 2nd Law,

and the definition of acceleration. Use F = ma with a = Δv/Δt .

7. Impulse is the product of the force acting on an object and the

time in which it acts. This gives us the formula for impulse which

is J = F·Δt. The unit of impulse in MKS is the Newton-second or Ns.

Impulse can also be derived by finding the area under a graph of

force versus time.

8. The Law of Conservation of Momentum states that "In a closed,

isolated system, the total momentum of the system does not change".

9. This law means that in all interactions between isolated objects,

momentum is conserved, or,  p_i = p_f  .

10. Objects can transfer momentum during collisions, but the total

momentum in the system before the collision must equal the total

momentum after the collision, again,  p_i = p_f  .

11. During a collision, the change in momentum of the first object is

equal to and opposite the change in momentum of the second object.

12. Collisions can be classified as elastic or inelastic based on

whether or not energy is also conserved. For the elastic collision we

have m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' . If the collision is inelastic we

have m₁v₁ + m₂v₂ = (m₁ + m₂)v_1,2 .

13. In a perfectly elastic collision, the momentum is conserved,

p_B = p_A   .

14. In a perfectly inelastic collision, two objects stick together and

move as one mass after the collision. The momentum is also

conserved, p_i = p_f   .

15. There is a special case called "recoil" in which, for example, two

objects are pushed against opposite ends of a spring. Clearly the

momentum before they are released is zero, so according to the

conservation law the momentum after they are released also must

be zero.

16. Recoil then is supported by the equation 0 = m₁v₁ + m₂v₂ ,

which requires that v₁ and v₂ must have opposite directions.

17. Realize that in the macro world, few collisions are perfectly elastic

or perfectly inelastic.

18. And still, we need these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct motion formula to use

(iv) use algebra to isolate the unknown

(v) substitute-in the given information and simplify.

Here are the answers to the homework problems:

Page 251:

#58. 74 kg m/s  10 m/s  #59. (a) 2.0x10⁴ kg m/s  (b) 1.3x10³ N

#61. -60 N       #64. 42 m/s 

#67. (a) -5.1 kg m/s   (b) -100 N  (c) -10 N

Page 253:

#76. -4.94 m/s   #80. 11 m/s   #83. 20.0 m/s

#84. (a) 2.12x10⁴ kg m/s     (b) 312 N

#85. (a) 2.35x10⁴ kg m/s    (b) 2.6x10⁴ N   (c) Friction

ARCHIVES:  CH.1     CH.2&3   CH.4&5  CH.6  Ch.7  Ch.8