chapter 07 impulse and momentum
TRANSCRIPT
Impulse and Momentum
ASTRONAUT Edward H. White II is in the zero gravity of space. By firing the gas-powered gun,
he gains momentum and maneuverability. Credit: NASA
Momentum DefinedMomentum is defined as the product of mass and velocity. (vector quantity) Units: kg m/s; g cm/s; slug ft/s
Momentum
m = 1000.0 kg ๐=(๐๐๐๐ .๐๐ค๐ ) (๐๐๐ฆ /๐ฌ )
๐=๐๐๐ฆ/๐ฌ๐=๐๐๐๐๐๐ค๐ ๐ฆ/๐ฌ
IMPULSE
Dt
Impulse:Impulse is a force acting for a small time interval Dt.
Example 1: The face of a golf club exerts an average force of 4000 N for 0.002 s. What is the impulse imparted to the ball?
Dt
Impulse:
The unit for impulse is the newton-second (N-s)
Other units are dyne-second and pound-second (lb-s)
In a ยฝ sheet of pad paper, discuss briefly the movie clip Spiderman 2 in the
application of impulse and momentum (their relationship):
Notice:
1. Train and its motion
2. How spiderman wants to stop the train using his legs, single shot of spiderweb
by each hand; and multiple shots of spiderwebs;
3. โstopperโ in the railroad.
Impulse Changes Velocity and Momentum
Consider a mallet hitting a ball:
Impulse = Change in โmvโImpulse = Change in โmvโ
Impulse and Momentum
Impulse = Change in momentum
Dt
F mv
A force F acting on a ball for a time Dt increases its momentum mv.
Conversion: 1.00 N.s = 1.00 kg m/s
Newtonโs Second Law of Motion
Example 3: A 50-g golf ball leaves the face of the club at 20 m/s. If the club is in contact for 0.002 s, what average force acted on the ball?
Dt
F mv
Given: m = 0.05 kg; vo = 0;
Dt = 0.002 s; v = 20 m/s+
Choose right as positive.
Average Force:
0
Vector Nature of Momentum
Consider the change in momentum of a ball that is dropped onto a rigid
plate:
vo
vA 2-kg ball strikes the plate with a speed of 20 m/s and rebounds with a speed of 15 m/s. What is the change in momentum?
+
Dp = mv - mvo
Dp = 70 kg m/s
Dp = 70 kg m/s
Dp = (2 kg)(15 m/s) - (2 kg)(-20 m/s)
Impulse = Change in momentumImpulse = Change in momentum
Momentum
Impulse
More Sample Problems: 1. A 0.10-kg ball is thrown straight up into the air
with an initial sped of 15 m/s. Find (a) the ballโs initial momentum; (b) its momentum at its maximum height; and (c) impulse of the weight on the ball from initial to maximum height.
2. The force shown in the force vs. time diagram acts on a 1.5 kg object. Find (a) the impulse of the force, (b) the final velocity of the object if it is initially at rest.
0.0 1.0 2.0 3.0 4.0 5.00.0
1.0
2.0
3.0Fx (N)
t (s)
๐จ๐=๐๐๐จ๐=
๐๐๐๐
Momentum is conserved in this rocket launch. The
velocity of the rocket and its
payload is determined by the mass and velocity of the
expelled gases. Photo:
NASA
Conservation of Linear Momentum
Conservation of Momentum
The total momentum of an isolated system of bodies remains constant.
system = set of objects that interact with each other.
An isolated system is one in which the only force present are those between the objects of the system; that is there is no net external
force.
therefore
๐ญ๐๐
๐ญ๐๐
๏ฟฝโ๏ฟฝ21=๐น 21 .โ ๐ก=๐1๐ฃ1โฒ โ๐1๐ฃ1
๏ฟฝโ๏ฟฝ12=๐น12 .โ ๐ก=๐2๐ฃ2โฒ โ๐2๐ฃ2
โด ๐21=โ ๐12
๐1๐ฃ1โฒ โ๐1๐ฃ1=โ (๐2๐ฃ2
โฒ โ๐2๐ฃ2 )
๐1๐ฃ1+๐2๐ฃ2=๐1๐ฃ1โฒ +๐2๐ฃ2
โฒ
Since
Initial momenta = final momenta
Conservation of Momentum
๐๐๐ฃ๐ โฒ ๐๐ ๐ฃ๐+๐๐๐ฃ๐=๐๐๐ฃ๐โฒ +๐๐๐ฃ๐
โฒ
๐๐ ๐ฃ๐ โฒSample Illustrations:
Initially, the system is at rest:
Rocket:
Gas:
๐ฃ๐โโฒ=โ
๐๐ ๐ฃ๐ โฒ
๐๐
Conservation of Momentum Revisited: Into Details
1 2๐๐๐๐ ๐๐๐๐
1 2๐๐๐๐ โฒ โ
1 2๐ญ๐๐
๐ญ๐๐
๐1๐ฃ1+๐2๐ฃ2=๐1๐ฃ1โฒ +๐2๐ฃ2
โฒ
APPLICATION: COLLISIONS and Conservation of Momentum
Simple Collisions (Head-on Collisions)
Example 01 A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2-kg physics book horizontally toward the north shore at a speed of 5.0 m/s. How long does it take him to reach the south shore?
A car with a mass of 9.00 x 102 kg is traveling at +15.0 m/s while an SUV with a mass of 1.80 x 103 kg is traveling at -15.0 m/s. (a) If the cars collide head-on, becoming entangled, find the velocity of the entangled cars after the collision. (b) If the SUV stops after collision and not entangled, what is the velocity of the car after collision?
Assignment:
1. What is the momentum of a 15-g sparrow flying with an initial speed speed of 12 m/s to the east? If the sparrow increases its speed to 14 m/s in the same direction, what is the impulse of its force?
2. Calculate the force exerted on a rocket, given that the propelling gases are expelled at a rate of 1000 kg/s with a speed of 60,000 m/s (at take off)
3. A 900-kg box car traveling at +20 m/s strikes a stationary second car. After collision, the box car stops and the second car travels with a velocity of +30 m/s. What is the mass of the second car?
Summary of Formulas:
Impulse = Change in momentumImpulse = Change in momentum
Momentum
Impulse
Conservation of MomentumConservation of Momentum
โ ๏ฟฝโ๏ฟฝ=๐ ;๐๐๐๐+๐๐๐๐=๐๐๐๐โฒ +๐๐
โฒ