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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 ??