a baseball (m = 153 g) approaches a bat horizontally at a speed of 41.0 m/s (92 mi/h) and is hit straight back at a speed of 45.8 m/s (102 mi/h). If the ball is in contact with the bat for a time of 1.05 ms, what is the average force exerted on the ball by the bat? Neglect the weight of the ball, since it is so much less than the force of the bat. Choose the direction of the incoming ball as the positive direction.
Thanks. I was messing up the change in velocity part
To find the average force exerted on the ball by the bat, we can use Newton's second law of motion which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration can be determined by the change in velocity and the time of contact.
Step-by-step solution:
1. Convert the speed of the ball into SI units (m/s). The speed of the ball before being hit is 41.0 m/s, and the speed of the ball after being hit is 45.8 m/s.
2. Convert the mass of the ball into SI units (kg). The mass of the ball is given as 153 g, which is equivalent to 0.153 kg.
3. Calculate the change in velocity. Since the direction of motion is reversed, the change in velocity is equal to the final velocity (45.8 m/s) minus the initial velocity (-41.0 m/s). It is negative because the direction is reversed. Therefore, the change in velocity is (-41.0 m/s) - (45.8 m/s) = -86.8 m/s.
4. Convert the time of contact into seconds. The given time of contact is 1.05 ms, which is equivalent to 1.05 × 10^(-3) s.
5. Calculate the acceleration. The acceleration can be determined using the equation: acceleration = change in velocity / time of contact. Therefore, the acceleration is (-86.8 m/s) / (1.05 × 10^(-3) s) = -82,666.7 m/s^2.
6. Finally, calculate the average force exerted on the ball by the bat using Newton's second law of motion: force = mass × acceleration. Substituting the values, we have force = (0.153 kg) × (-82,666.7 m/s^2) ≈ -12,657.88 N.
The average force exerted on the ball by the bat is approximately -12,657.88 N. The negative sign indicates that the force is in the opposite direction of the positive direction chosen earlier.
force*time= mass(change velocity)
= mass(-45.8- (+41))= -mass*86.5
solve for force