Question

A truck was driving on a highway at 30 m/s when its brakes gave out. The driver steered it onto a "runaway truck ramp", consisting of an upward ramp (rising 12 meters vertically over 120 meters horizontally), and ending with a compressible barrier which you can model as a giant spring with spring constant "k". The compressible barrier can be compressed by a maximum 0.5 meters before it stops working.

Answer 1

The physics question involves analyzing the motion of a truck with failed brakes using energy conservation, kinematics, and Hooke's law to determine if a ramp and spring can stop it effectively.

Step-by-step explanation:

The subject of the question involves a truck's motion and its interaction with physics concepts such as energy, force, and motion on a runaway ramp. Utilizing principles such as conservation of energy, the force exerted by a spring, and kinematics, we can analyze the truck's behavior as it ascends the ramp and compresses the barrier spring. Specifically, considering a truck initially moving at 30 m/s when the brakes fail and how its motion can be halted using a ramp and a spring allows us to apply mechanics to a real-life problem.

For instance, we can calculate the amount of kinetic energy the truck has when entering the ramp, how much potential energy it gains as it moves up the ramp, and the work done by the spring when it halts the truck. The effectiveness of the spring in stopping the truck can also be determined by using Hooke's law and the concept of spring compression. This integration of different physics concepts creates a comprehensive analysis of the situation.