A 8.5-kg bowling ball is rolling down the alley with a velocity of 3.5 m/s. For each impulse, a and b, as shown below, find the resulting speed and direction of motion of the bowling ball.
To find the resulting speed and direction of motion of the bowling ball after each impulse, we need to apply the law of conservation of linear momentum. The law states that the total momentum of a system remains constant if no external forces act on it. In this case, we consider the system to be the bowling ball.
The formula for momentum is:
Momentum = mass × velocity
Let's denote the initial momentum of the bowling ball as P1, and the final momentum after each impulse as P2.
Initial momentum: P1 = mass × initial velocity = 8.5 kg × 3.5 m/s = 29.75 kg·m/s
Impulse a: The magnitude of impulse is given in the diagram as 20 N·s to the right. Impulse is defined as the change in momentum, so we can calculate the final momentum after impulse a:
Magnitude of impulse a = change in momentum = P2 - P1
P2 = P1 + Magnitude of impulse a
P2 = 29.75 kg·m/s + 20 N·s = 49.75 kg·m/s
The speed and direction of motion after impulse a are determined by the final momentum:
Speed = P2 / mass = 49.75 kg·m/s / 8.5 kg ≈ 5.85 m/s
Direction of motion: The impulse a is applied to the right, so the direction of motion after impulse a will be to the right.
Impulse b: The magnitude of impulse b is given in the diagram as 25 N·s to the left. Similar to impulse a, we can calculate the final momentum after impulse b:
Magnitude of impulse b = change in momentum = P2 - P1
P2 = P1 - Magnitude of impulse b
P2 = 29.75 kg·m/s - 25 N·s = 4.75 kg·m/s
The speed and direction of motion after impulse b can be determined using the final momentum:
Speed = P2 / mass = 4.75 kg·m/s / 8.5 kg ≈ 0.56 m/s
Direction of motion: The impulse b is applied to the left, so the direction of motion after impulse b will be to the left.
Nothing is "shown below"
A 8.5-kg bowling ball is rolling down the alley with a velocity of 3.5 m/s. For each impulse, a and b, as shown below, find the resulting speed and direction of motion of the bowling ball.
(a) find the resulting speed and direction of motion of the bowling ball.