A car moving at 10.0 m / s crashes into a barrier and stops in 0.050 s. There is a 20.0 -kg chil

step 1 Here for part A, this would be the before and after situation, essentially for the system. We ha

A car moving at 10.0 m / s crashes into a barrier and stops...

A car moving at $10.0 \mathrm{m} / \mathrm{s}$ crashes into a barrier and stops in 0.050 s. There is a 20.0 -kg child in the car. Assume that the child's velocity is changed by the same amount as that of the car, and in the same time period. a. What is the impulse needed to stop the child? b. What is the average force on the child? c. What is the approximate mass of an object whose weight equals the force in part b? d. Could you lift such a weight with your arm? e. Why is it advisable to use a proper restraining seat rather than hold a child on your lap?

A car moving at $10.0 \mathrm{m} / \mathrm{s}$ crashes into a barrier and stops in 0.050 s. There is a 20.0 -kg child in the car. Assume that the child's velocity is changed by the same amount as that of the car, and in the same time period.
a. What is the impulse needed to stop the child?
b. What is the average force on the child?
c. What is the approximate mass of an object whose weight equals the force in part b?
d. Could you lift such a weight with your arm?
e. Why is it advisable to use a proper restraining seat rather than hold a child on your lap?

Key Concepts

Impulse-Momentum Theorem

The impulse-momentum theorem states that the impulse applied to an object is equal to the change in its momentum. In other words, when a force is applied over a certain time interval, it results in a change in the object's velocity. This theorem forms the basis for calculating quantities such as the impulse needed to stop an object or change its speed, using the relationship Impulse = Change in Momentum.

Average Force

Average force is derived by dividing the total impulse by the time interval over which the force acts. This concept is crucial when forces vary over time, as it provides a simplified measure of the force that produces the same overall change in momentum. Understanding average force helps in analyzing impact situations where forces are exerted rapidly and non-uniformly.

Mass-Weight Relationship

The mass-weight relationship explains that an object's weight is the force exerted on it by gravity, calculated by multiplying its mass by the acceleration due to gravity. This concept is important in contexts where forces are equated to weights (such as comparing the force experienced during an impact to the gravitational force on a given mass), thereby allowing comparisons and understanding of human lifting capacities or the effects of impact forces in everyday terms.

Safety Restraints

Safety restraints are devices or mechanisms designed to secure occupants in vehicles to minimize injury during abrupt deceleration or collisions. The use of a proper restraining seat ensures that forces are distributed over a larger area of the body and controlled deceleration minimizes the risk of injury. This concept highlights the importance of reducing rapid momentum changes on the body through proper safety equipment rather than relying on less secure methods such as holding a child in one's lap.

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