Question

Sarah, who has a mass of 55 kg, is riding in a car at 20 m/s. She sees a cat crossing the street and slams on the brakes! Her seatbelt stops her from flying forward, bringing her to rest in 0.5 seconds. How much force did the seatbelt put on Sarah?

A. 220 N
B. 440 N
C. 550 N
D. 660 N

A big-league hitter attacks a fastball! The ball has a mass of 0.16 kg. It is pitched at 38 m/s. After the player hits the ball, it is now traveling 44 m/s in the opposite direction. The impact lasted 0.002 seconds. How big of a force did the ballplayer put on that ball?

A. 400 N
B. 800 N
C. 1200 N
D. 1600 N

Someone fires a 0.04 kg bullet at a block of wood that has a mass of 0.5 kg. (The block of wood is sitting on a frictionless surface, so it moves freely when the bullet hits it). The wood block is initially at rest. The bullet is traveling 300 m/s when it hits the wood block and sticks inside it. Now the bullet and the wood block move together as one object. How fast are they traveling?

A. 2 m/s
B. 3 m/s
C. 4 m/s
D. 5 m/s.

Answer 1

The force the seatbelt put on Sarah is 2200 N. The force the baseball player put on the ball is 6560 N. The speed of the wood block and bullet moving together is approximately 22 m/s.

Step-by-step explanation:

To calculate the force the seatbelt put on Sarah, we use the change in momentum over time, which is also known as impulse. Sarah's velocity changed from 20 m/s to 0 m/s in 0.5 seconds. The formula to calculate force (F) is F = Δp / Δt = m * Δv / Δt. Therefore, F = (55 kg * (0 - 20 m/s)) / 0.5 s = -1100 N / 0.5 s = -2200 N. Since force is a vector and has direction, the negative sign indicates the force is in the opposite direction of motion, but in terms of magnitude, the answer is B. 2200 N.

To find the force that the baseball player put on the ball, the change in the ball's velocity is from 38 m/s (pitched) to 44 m/s (opposite direction after hit), so the total change is 38 + 44 = 82 m/s. Using the same formula, F = (0.16 kg * 82 m/s) / 0.002 s = 6560 N. Therefore, the force is D. 6560 N.

Finally, to find the speed of the wood block and the bullet moving together, use the conservation of momentum principle because no external forces are acting on the system. The total momentum before the collision (bullet's momentum) must equal the total momentum after (the combined mass of bullet and block). So, (0.04 kg * 300 m/s) = (0.04 kg + 0.5 kg) * v. Solving for v gives v = (0.04 kg * 300 m/s) / (0.54 kg) ≈ 22.22 m/s. Given the options, the closest answer is D. 22 m/s.