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Type: Single
Date: ______________
Objective: Impulse and Momentum I
Homework: Assignment (1-28)
Read 7.1, Do Concept QUEST (8),
Do PROBS # (3, 7) Ch. 7
AP Physics “B”
Mr. Mirro
Date: ________
Impulse and Momentum I
There are many situations in which the force acting on an object is NOT constant, but varies with time.
So far, we have discussed the behavior several such devices - such as cross bows and spring systems.
Now, let’s consider the effects of hitting a baseball.
FIRST: When the bat strikes the ball, the magnitude of
the force exerted on the ball rises to a “maximum” value
and then returns to zero when the ball leaves the bat.
SECOND: The time interval (or duration) during which the force
acts is Δt, and the magnitude of the average force is Favg.
If a baseball is to be hit “WELL”, both the size of the force and the time of contact are important.
Therefore, when a large average force acts on the ball for a long enough time, the ball is
considered to be hit “SOLIDLY” …
In other words, there was a large CHANGE IN “MOMENTUM” !!
Consider the Force versus Time graph below where the area under the curve represents the “impulse” or
change in momentum.
DefN: Impulse-Momentum
The impulse of a force is the product of the average force and the time interval during which the
force acts:
Impulse ⇒ Favg Δt
Impulse is a “vector” quantity and has the same direction as the average force.
When a ball is hit, it responds to the value of the impulse.
‰
A small impulse produces a small response
‰
A large impulse produces a large response
That is, a large impulse which produces a large response causes the ball to depart from the bat
with a large velocity.
However, we know from experience that the more massive the ball, the less velocity it has after leaving
the bat. So both mass and velocity play a role in how an object responds to a given impulse.
The effect of mass and velocity is included in the concept of linear momentum which goes as follows:
DefN: Linear Momentum
The linear momentum of an object is the product of the object’s mass and velocity.
p = mv
Linear momentum is a “vector” quantity that points in the same direction as the velocity.
According to Newton’s Second Law, the cause of the average acceleration is an average net
force FNet = ma.
FNet = m [vf - vi]
Δt
where a = Δv
Δt
Which leads us to the Impulse-Momentum Theorem, which states:
DefN: Impulse-Momentum ThM
When a net force acts on an object, the impulse of the net force is equal to the change in momentum
of the object:
Favg Δt = m Δv = mvF - mvi
Where the Impulse ⇔ Change in Momentum
AP Physics “B”
Mr. Mirro
Date: ________
Impulse and Momentum I
Ex 1: A base ball of mass m = 0.14 kg, has an initial velocity v0 = -38 m/s as it approaches a bat. The
bat 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 vF = + 58 m/s. [Note: Direction of approach taken as negative direction.]
[Cutnell7.1]
a. Determine the impulse applied to the ball by the bat.
b. Assuming that the time of contact was Δt = .0016 sec (1.6 milli-seconds), find the average net
force exerted on the ball by the bat.
Ex 2: A 10 kg watermelon is dropped straight down into the water from a diving platform. Just before
striking the water, the watermelon’s speed is 9.0 m/s. After entering the water, the speed of the
watermelon is reduced to 1.0 m/s by an average force of 160 N. [CutnellP7.3sim]
a. How long did it take the watermelon to reach this speed after entering the water ?
b. How long did it take the watermelon to come to rest in the water ?
Ex 3: A woman driving a golf gall off a tee, applies an average force of 200 N thereby giving the ball
an initial velocity v0. The mass of the ball is 0.045 kg, and the duration of the impact with the
golf club is 6 x 10-3 sec. Determine the initial speed of the ball after impact. [Cutnell4EP7.6sim]
Ex 4: A skater is standing still in front of a wall. By pushing against the wall she propels herself
backward with a velocity of -1.2 m/s. Her hands are in contact with the wall for 8.0 sec.
If the magnitude of her average force on the wall is 7.0 N, find the mass of the skater.
[CutnellP7.7sim]
Note: Ignore friction, wind resistance and the vibrational effects of stampeding elephants.
Ex 5: An object of mass 1 kg is dropped from rest. At the instant the object hits the ground the
magnitude of its momentum is 2 kg m/s. Determine the speed of the object just before impact.
[CutnellP7.10sim]
Challenge: From what height was this object dropped ??