The average net force required to stop a 3.5 kg bowling ball initially traveling at 1.5 m/s over a distance of 0.4 m is 9.84375 N, directed opposite to the ball's initial motion.
To calculate the average net force required to stop a 3.5 kg bowling ball, we can use the work-energy principle.
The work done by the stopping force is equal to the change in kinetic energy of the bowling ball.
The initial kinetic energy (KE) of the bowling ball is given by (1/2)mv², where m is the mass of the ball and v is its initial velocity.
KE_initial = (1/2)(3.5 kg)(1.5 m/s)² = 3.9375 J
Since the ball comes to a stop, its final kinetic energy is 0 J. The work done (W) by the force to stop the ball is equal to this change in kinetic energy, which is -3.9375 J (negative because the ball is slowing down).
W = -KE_initial = -3.9375 J
Work is also equal to the force times the distance (W = Fd), so we can solve for the average force (F).
-3.9375 J = F(0.4 m)
F = -3.9375 J / 0.4 m = -9.84375 N
The negative sign indicates that the force is in the opposite direction of the ball's initial motion. Hence, the magnitude of the average net force required is 9.84375 N.