Question

1. an automobile with a mass of 1000 kg is moving at 20 m/s (approximately 40 mi/h). its momentum is p = mv p = (1000 kg)(20 m/s) p = 20,000 kg*m/s the approximate mass of the following objects is given in kilograms. calculate how fast (in m/s) each object would have to be traveling to have the same momentum as the automobile. a. truck (10,000 kg) b. bicycle (8 kg) c. bowling ball (2.85 kg) d. baseball (0.145kg) 5. a small sports car hits a heavy truck in a collision. what factors determine the outcome for the passengers of the two vehicles? which driver will sustain worse injuries? why?

Explanation:

Step1: Rearrange the momentum formula

Given \(p = mv\), we can solve for \(v\) as \(v=\frac{p}{m}\). The momentum of the automobile \(p = 20000\space kg\cdot m/s\) (from \(p=(1000\space kg)(20\space m/s)\))

Step2: Calculate for the truck

For the truck with \(m = 10000\space kg\), \(v=\frac{20000\space kg\cdot m/s}{10000\space kg}=2\space m/s\)

Step3: Calculate for the bicycle

For the bicycle with \(m = 8\space kg\), \(v=\frac{20000\space kg\cdot m/s}{8\space kg}=2500\space m/s\)

Step4: Calculate for the bowling ball

For the bowling ball with \(m = 2.85\space kg\), \(v=\frac{20000\space kg\cdot m/s}{2.85\space kg}\approx 7017.54\space m/s\)

Step5: Calculate for the baseball

For the baseball with \(m = 0.145\space kg\), \(v=\frac{20000\space kg\cdot m/s}{0.145\space kg}\approx 137931.03\space m/s\)

• Factors determining the outcome: The mass and velocity of the vehicles (related to momentum), the design of the vehicles (crumple zones, seat - belts, airbags), and the duration of the collision (impulse \(J = F\Delta t\)).
• Which driver will sustain worse injuries: The driver of the small sports car. According to Newton's third law, the force exerted on both vehicles is the same in magnitude during the collision. But from \(F = ma\) (where \(a=\frac{\Delta v}{\Delta t}\)), for the same force \(F\), a smaller - mass vehicle (sports car) will have a larger acceleration (change in velocity per unit time). Larger accelerations (decelerations in this case) lead to more severe injuries as per the relationship between force, mass, and acceleration.

Answer:

a. \(2\space m/s\)
b. \(2500\space m/s\)
c. \(\approx 7017.54\space m/s\)
d. \(\approx 137931.03\space m/s\)

For question 5: