Trains

Momentum Which hurts more if it hits you? Why? Left one has more mass Left one has more velocity Left one has more momentum!

Momentum What does the word momentum mean to you? What does the word momentum mean to you? Newton referred to what modern physicists term linear momentum as “the quantity of motion…arising from velocity and the quantity of matter conjointly.” Newton referred to what modern physicists term linear momentum as “the quantity of motion…arising from velocity and the quantity of matter conjointly.” In other words, the momentum of the body is proportional to both its mass and its velocity. By definition, In other words, the momentum of the body is proportional to both its mass and its velocity. By definition, p = mv It is a vector quantity that has units of a kgm/s. (There’s no short version, like with Force and Energy)

Newton’s Second Law If an object has a change in velocity, a net force must be acting on it. If an object has a change in velocity, a net force must be acting on it. Similarly, since momentum is directly related to velocity (as well as mass), a change in momentum also requires a net force. Similarly, since momentum is directly related to velocity (as well as mass), a change in momentum also requires a net force. In fact, Newton originally expressed his second law of motion in terms of momentum rather than acceleration. In fact, Newton originally expressed his second law of motion in terms of momentum rather than acceleration.

Change in Momentum Newton’s second law states that the net external force acting on an object is equal to the time rate of change of the object’s momentum. Newton’s second law states that the net external force acting on an object is equal to the time rate of change of the object’s momentum.

Hammering a Nail…

Impulse When two objects—such as a hammer and a nail, a golf club and a golf ball, or even two cars—collide, they can exert large forces on one another for a short period of time. When two objects—such as a hammer and a nail, a golf club and a golf ball, or even two cars—collide, they can exert large forces on one another for a short period of time. The force is not constant in this case. However, Newton’s second law in momentum form is still useful for analyzing such situations by using average values. The force is not constant in this case. However, Newton’s second law in momentum form is still useful for analyzing such situations by using average values. Written in this form, the law states that the net average force is equal to the time rate of change of momentum: F = Δp/Δt. Written in this form, the law states that the net average force is equal to the time rate of change of momentum: F = Δp/Δt. Rewriting the equation to express the change in momentum, we have Rewriting the equation to express the change in momentum, we have FΔt = Δp = p - p o

Impulse The term FΔt is known as the impulse of the force: Impulse = FΔt = Δp = mv – mv o The SI unit of impulse is a Ns. Thus, the impulse exerted on a body is equal to the change in the body’s momentum. Why are you always instructed to “follow through” in sports?

Baseball Who exerts the greater impulse on a baseball…the pitcher or the catcher? Who exerts the greater impulse on a baseball…the pitcher or the catcher? Who exerts the greater force on a baseball…the pitcher or the catcher? Who exerts the greater force on a baseball…the pitcher or the catcher?

Pitchers and Catchers Catcher: High force, short time Ergo: Big mitt. Pitcher: Low force, long time

Air Bags

In an accident, the magnitude of the acceleration is about 32 g’s. Such an acceleration means a net force about 32 times the weight of the dummy, clearly enough to cause serious injuries. In an accident, the magnitude of the acceleration is about 32 g’s. Such an acceleration means a net force about 32 times the weight of the dummy, clearly enough to cause serious injuries. What does an air bag do? What does an air bag do? Increases the stopping distance (increase stopping time). Increases the stopping distance (increase stopping time). Allows the force to be distributed over a much larger area (more on this later). Allows the force to be distributed over a much larger area (more on this later).

Air Bags can be dangerous too!

More with Air Bags The first graph shows the average force on a dummy as a function of a stopping distance. With no seat belt or air bag, you either fly through the windshield, or are stopped in a fraction of a meter by the dashboard or steering wheel. The first graph shows the average force on a dummy as a function of a stopping distance. With no seat belt or air bag, you either fly through the windshield, or are stopped in a fraction of a meter by the dashboard or steering wheel. The next graph shows the force as a function of the initial velocity for three stopping distances. The next graph shows the force as a function of the initial velocity for three stopping distances. Why is it curved? Why is it curved? Think of energy here people. Think of energy here people. Air bags can hurt, too…how? Air bags can hurt, too…how?

Problem #1 A woman, driving a golf ball off a tee, gives the ball a velocity of 28 m/s. The mass of the ball is kg, and the duration of the impact with the golf club is 6 ms. (a) What is the change in momentum of the ball? (b) Determine the average force applied to the ball by the club? A woman, driving a golf ball off a tee, gives the ball a velocity of 28 m/s. The mass of the ball is kg, and the duration of the impact with the golf club is 6 ms. (a) What is the change in momentum of the ball? (b) Determine the average force applied to the ball by the club? Answer: Answer: 1.3 kgm/s 1.3 kgm/s 220 N 220 N

Problem #2 A baseball (m=0.14 kg) has an initial velocity of v o = 38 m/s as it approaches the bat. The applies a force that is much larger than the weight of the ball, and the ball departs from the bat with a final velocity of v f = 58 m/s. The contact time between the bat and ball is Δt = 4.0 x s. Find the average force exerted on the ball by the bat. A baseball (m=0.14 kg) has an initial velocity of v o = 38 m/s as it approaches the bat. The applies a force that is much larger than the weight of the ball, and the ball departs from the bat with a final velocity of v f = 58 m/s. The contact time between the bat and ball is Δt = 4.0 x s. Find the average force exerted on the ball by the bat. Answer: Answer: 3400 N 3400 N