5. An object with a mass of 70 kilograms hits a stationary air bag, with velocity 25 m/s at
the instant of impact. After 0.25 seconds the object has come to a stop and the air bag has
deflated. The average force on object during this interval is most nearly,
a. 70,000 N
b. 7,000 N
c. 700 N
d. 70 N
Introduction
Calculating average force is a fundamental concept in physics, especially in collision scenarios such as airbag impacts. This article explains the formula for average force and demonstrates its application with a detailed example involving a 70 kg object hitting an airbag.
Step-by-Step Solution
Given:
- Mass (m) = 70 kg
- Initial velocity (vi) = 25 m/s
- Final velocity (vf) = 0 m/s
- Time interval (Δt) = 0.25 s
Substitute the values:
F = 70(0 − 25) / 0.25 = −7000 N
The negative sign indicates that the force acts opposite to the direction of motion.
The magnitude of the average force is 7000 N.
Explanation of Options
- a. 70,000 N: Ten times higher than the calculated value — incorrect.
- b. 7,000 N: Matches the calculated value — correct answer.
- c. 700 N: Ten times smaller — incorrect.
- d. 70 N: Hundred times smaller — incorrect.
Physics Behind the Formula
The average force during a collision is determined by the change in momentum over time:
In this example, a 70 kg object moving at 25 m/s comes to rest in 0.25 s due to an airbag. The airbag increases the time of impact, which significantly reduces the average force — minimizing injury risk. This principle forms the basis of many safety devices in vehicles.
Conclusion
Understanding how to calculate average force helps in analyzing real-world physics problems, from car crashes to sports impacts. The formula offers a simple yet powerful way to predict collision effects and design safer systems. In this example, the calculated force of 7000 N demonstrates how extending impact time, as airbags do, can save lives.
