1. Impulse – Change of Momentum theorem
Q: Why does the bat shatter sometimes?
Video: Physics of Baseball Pitches. Discuss.

2. IMPULSE
Impulse J is a force F acting for a small time interval Dt. F Dt
Impulse:
J = FDt
Q: What is the metric unit of impulse?
Ns

3. Example 1: The face of a golf club exerts an average force of 4000 N for s. What is the impulse imparted to the ball? Dt F
Impulse:
J = F  Dt
J = (4000 N)(0.002 s)
J = 8.00 Ns
The unit for impulse is the Newton second (N s)

4. 𝑱= 𝑭 𝒂𝒗𝒈 ∙∆𝒕 ∆𝑡= 𝐽 𝐹 𝑎𝑣𝑔 = −5𝑁∙𝑠 −1200𝑁
Example 2: Two flexible balls collide. The ball B exerts an average force of 1200 N on ball A. How long were the balls in contact if the impulse is 5 Ns? B A
𝑱= 𝑭 𝒂𝒗𝒈 ∙∆𝒕
∆𝑡= 𝐽 𝐹 𝑎𝑣𝑔 = −5𝑁∙𝑠 −1200𝑁
Dt = s
The impulse is negative; the force on ball A is to the left. Unless told otherwise, treat forces as average forces.

5. Momentum Defined v = 16 m/s p = mv
Momentum p is a vector quantity, defined as the product of mass and velocity, mv. Units of momentum are: kgm/s
Momentum is also called the amount of motion.
p = mv
m = 1000 kg
v = 16 m/s
p = (1000 kg)(16 m/s)
p = 16,000 kg m/s

6. Impulse Changes Velocity
Consider a mallet hitting a ball: F
𝑎= 𝐹 𝑚
𝐹 𝑚 = ∆𝑣 ∆𝑡
𝑎= ∆𝑣 ∆𝑡
𝐹∆𝑡=𝑚∆𝑣=∆ 𝑚𝑣 =∆𝑝
Impulse = Change in “mv”

7. Impulse and Momentum Impulse = Change in momentum 𝑱=∆𝒑
𝑭∆𝒕=𝒎 𝒗 𝒇 −𝒎 𝒗 𝒊 Dt F
A force F acting on a ball initially at rest, for a time Dt, increases its momentum mv. mv

8. Examples of time interval ∆𝒕
𝑱=∆𝒑
𝑭∆𝒕=𝒎 𝒗 𝒇 −𝒎 𝒗 𝒊

9. Choose right as positive.
Example 3: A 50-g golf ball leaves the face of the club at 20 m/s. If the club is in contact for s, what average force acted on the ball?
Given: m = 0.05 kg; vi = 0;
Dt = s; vf = 20 m/s Dt F mv +
Choose right as positive.
F Dt = mvf - mvi
F (0.002 s) = (0.05 kg)(20 m/s)
Average Force:
F = 500 N

10. Directions Are Essential
1. Choose and label a positive direction. + vf vi
2. A velocity is positive when it points along this direction and negative when it points against it.
Assume vi is 30 m/s to the left and vf is 10 m/s to the right. What is the change in velocity Dv?
vf = +10 m/s
vi= -30 m/s
vf – vi = (10 m/s) – (-30 m/s)

11. Example 4: A 500-g baseball moves to the left at 20 m/s striking a bat
Example 4: A 500-g baseball moves to the left at 20 m/s striking a bat. The bat is in contact with the ball for s, and it leaves in the opposite direction at 40 m/s. What was average force on ball? + Dt F
40 m/s
20 m/s
m = 0.5 kg + -
F Dt = mvf - mvi
vi = -20 m/s; vf = 40 m/s
F(0.002 s) = (0.5 kg)(40 m/s) - (0.5 kg)(-20 m/s)
Continued . . .

12. + Example 4 (continued): - m = 0.5 kg F 40 m/s 20 m/s Dt
F Dt = mvf - mvi
F(0.002 s) = (0.5 kg)(40 m/s) - (0.5 kg)(-20 m/s)
F(0.002 s) = (20 kg m/s) + (10 kg m/s)
F = 15,000 N
F(0.002 s) = 30 kg m/s