Final answer:
The magnitude of the force exerted on the golf ball by the window is calculated using the change in momentum and the time interval. By determining the change in momentum as a result of the change in velocity and dividing by the time the force was applied, the force is found to be 358.53 N.
Step-by-step explanation:
The student's question pertains to determining the magnitude of the force exerted on a golf ball by a window, given the ball's change in velocity during the collision. The concept in physics relevant to this question is impulse and the law of conservation of momentum. The force can be calculated using the formula F = Δp / Δt, where Δp is the change in momentum and Δt is the time over which the force is applied.
To begin, we calculate the change in momentum of the golf ball. The initial momentum, pi, is the product of the initial mass and velocity, pi = m × vi. The final momentum, pf, is the product of the mass and the final velocity, pf = m × vf. The change in momentum, Δp, is then pf − pi.
The mass of the golf ball is 0.023 kg, the initial velocity is 15.3 m/s, and the final velocity is 10.0 m/s. Using these values, we find: pi = 0.023 kg × 15.3 m/s = 0.3519 kg·m/s and pf = 0.023 kg × 10.0 m/s = 0.230 kg·m/s. Thus, the change in momentum is Δp = 0.230 kg·m/s − 0.3519 kg·m/s = −0.1219 kg·m/s (taking direction into account).
Now that we have Δp, we divide it by the time interval Δt, which is 3.4 × 10⁻⁴ s, to find the force: F = −0.1219 kg·m/s / 3.4 × 10⁻⁴ s = −358.53 N. Since force is a vector quantity, the negative sign represents the direction opposite the motion of the golf ball, meaning the force is exerted on the golf ball in the direction back towards the window. Given the context, however, the question asks for the magnitude of the force, thus we can report the answer as 358.53 N.