Question

Show Your Work On How You Got The Answer.

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) 2200 N
b) 1100 N
c) 220 N
d) 44 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) 360 N
b) 240 N
c) 60 N
d) 120 N

Answer 1

Sarah experienced a force of 2200 N from her seatbelt when she braked, calculated using Newton's second law. The baseball scenario contains an inconsistency, as the calculated force is 6560 N, which does not match any of the provided options.

Step-by-step explanation:

To calculate the force exerted by the seatbelt on Sarah, we use Newton's second law of motion, which states that force is the product of mass and acceleration (F = ma).

Sarah's deceleration (a) can be determined using the formula: a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time taken to stop. We are given that Sarah was initially travelling at 20 m/s (vi = 20 m/s), comes to rest (vf = 0 m/s), and she stops in 0.5 seconds (t = 0.5 s).

So, a = (0 - 20) m/s / 0.5 s = -40 m/s². The negative sign indicates a deceleration.

Using Sarah's mass of 55 kg, the force can be calculated as: F = ma = 55 kg * -40 m/s² = -2200 N.

The force is negative because it is in the opposite direction of Sarah's motion, but since we are interested in the magnitude, the answer is 2200 N.

The same principle is applied for the baseball scenario. Change in velocity is from -38 m/s (the negative sign indicates the initial direction) to 44 m/s, so the total change is (44 - (-38)) m/s = 44 + 38 m/s = 82 m/s. The time of impact is 0.002 seconds. So acceleration a = 82 m/s / 0.002 s = 41000 m/s².

Using the mass of the ball (0.16 kg), the force exerted is: F = ma = 0.16 kg * 41000 m/s² = 6560 N. However, we don't have this option, which suggests there might be a mistake either in the given data or in the options provided. Normally you would discuss this discrepancy with your tutor or teacher.