Final answer:
The ball's change in momentum is -0.68 kg*m/s, and the average force exerted by the wall on the ball is -6.8 N, indicating the force direction is opposite to the ball's initial motion.
Step-by-step explanation:
The change in momentum of a ball can be calculated using the formula for impulse, which is the product of the average force exerted on an object and the time interval during which the force acts. The ball's momentum changes because it impacts the wall and bounces back. This situation involves not only a change in the speed of the ball but also a change in the direction of its velocity, which we consider negative after the bounce insofar as velocity is a vector quantity.
To determine the ball’s change in momentum, we first find the initial and final momenta. The initial momentum (p_i) is the product of the mass (m) and the initial velocity (v_i), so p_i = m * v_i = 40 g * 10 m/s (remembering to convert grams to kilograms, so the mass should be 0.040 kg). The final momentum (p_f) similarly is p_f = m * v_f = 0.040 kg * -7 m/s (the velocity is negative because the direction has changed). The change in momentum (Δp) is the final momentum minus the initial momentum, so Δp = p_f - p_i = (0.040 kg * -7 m/s) - (0.040 kg * 10 m/s) = -0.28 kg*m/s - 0.4 kg*m/s = -0.68 kg*m/s.
To find the average force between the ball and the wall during the bounce, we use the impulse-momentum theorem, which states that the impulse is equal to the change in momentum. The impulse is also the product of the force and the time interval (F * Δt), so we can rearrange the equation to solve for the force (F). Knowing the change in momentum (Δp = -0.68 kg*m/s) and the time interval (Δt = 0.1 s), we can calculate the force as F = Δp / Δt = -0.68 kg*m/s / 0.1 s = -6.8 N. The negative sign indicates the force is in the opposite direction of the initial motion of the ball.