Answer:
The number of hailstones striking the window per unit time is:
n = 580 hailstones / 41 s = 14.1463 hailstones/s
The mass of each hailstone is 7 g = 0.007 kg, and its speed is 6.7 m/s. The kinetic energy of each hailstone is:
K = (1/2) * m * v^2 = (1/2) * 0.007 kg * (6.7 m/s)^2 = 0.167 N*m
The angle of incidence is 31°, so the angle between the hailstones and the normal to the window is 59°. The average force on the window is the rate of change of momentum of the hailstones. The momentum of each hailstone before the collision is:
p1 = m * v * cos(59°) * (-i) + m * v * sin(59°) * j
where i and j are the unit vectors in the x- and y-directions, respectively. The negative sign in front of the i-vector indicates that the hailstone is moving to the left (in the negative x-direction).
The momentum of each hailstone after the collision is:
p2 = m * v * cos(59°) * i + m * v * sin(59°) * j
The change in momentum of each hailstone is:
Δp = p2 - p1 = 2 * m * v * cos(59°) * i
The rate of change of momentum (i.e., the force) is:
F = n * Δp / Δt
where Δt is the time for each hailstone to strike the window. This time is equal to the width of the window divided by the component of the velocity perpendicular to the window, which is:
Δt = 1.346 m / (v * sin(59°)) = 1.346 m / (6.7 m/s * sin(59°)) = 0.139 s
Substituting the values, we get:
F = 14.1463 hailstones/s * 2 * 0.007 kg * 6.7 m/s * cos(59°) * (-i) / 0.139 s
F = 28.051 N * i
Therefore, the average force on the window is 28.051 N, in the negative x-direction.
Step-by-step explanation: