A student proposes a design for an automobile crash barrier...

A student proposes a design for an automobile crash barrier in which a 1700 -kg sport utility vehicle moving at 20.0 $\mathrm{m} / \mathrm{s}$ crashes into a spring of negligible mass that slows it to a stop. So that the passengers are not injured, the acceleration of the vehicle as it slows can be no greater than 5.00$g .$ (a) Find the required spring constant $k,$ and find the distance the spring will compress in slowing the vehicle to a stop. In your calculation, disregard any deformation or crumpling of the vehicle and the friction between the vehicle and the ground. (b) What disadvantages are there to this design?

A student proposes a design for an automobile crash barrier in which a 1700 -kg sport utility vehicle moving at 20.0 $\mathrm{m} / \mathrm{s}$ crashes into a spring of negligible mass that slows it to a stop. So that the passengers are not injured, the acceleration of the vehicle as it slows can be no greater than 5.00$g .$ (a) Find the required spring constant $k,$ and find the distance the spring will
compress in slowing the vehicle to a stop. In your calculation, disregard any deformation or crumpling of the vehicle and the friction between the vehicle and the ground. (b) What disadvantages are there to this design?

Key Concepts

Acceleration Constraints

In the context of safety and impact design, setting limits on acceleration (or deceleration) is crucial to protect occupants or structural integrity. Maximum acceleration limits ensure that forces experienced during rapid deceleration do not exceed safe thresholds, which are critical in evaluating designs for crash barriers or other energy-absorbing systems.

Design Trade-offs in Energy Absorption

When designing systems to absorb kinetic energy and protect against injury, trade-offs must be considered. While a spring can provide a controlled way to decelerate an object by absorbing energy, factors such as the physical size of the deformation, potential for rebound, material fatigue, and overall system integration must be balanced against the need for a safe and effective energy absorption mechanism.

Conservation of Energy

This concept involves equating the kinetic energy of a moving object to another form of energy—in this case, the potential energy stored in a spring when it is compressed. In collision problems, the energy initially present in the moving object is converted completely into another form (assuming no losses), which is a fundamental principle used to determine parameters such as spring constant or compression distance.

Hooke's Law

Hooke's Law is central to understanding how springs behave under load, stating that the force exerted by a spring is directly proportional to its displacement from the equilibrium position, within the elastic limit. This relationship (F = -kx) provides the basis for calculating how much energy a spring can store when it is compressed and how it will react to an applied force.

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