Three cars with identical engines and tires start from rest, and accelerate at their maximum rate. Car X is the most massive, an
d car Z is the least massive. Which car needs to travel the farthest before reaching a speed of 60 mi/h? A. Car Z
B. Car Y
C. Car X
D. All cars need to travel the same distance, although some cars will take longer than other cars.
any law stating that some quantity or property remains constant during and after an interaction or process, as conservation of charge or conservation of linear momentum.
Assuming that we can neglect the gravitational potential energy of the mass, and that no other forces acting on the payload, total mechanical energy must be conserved.
This energy, at any time, is part elastic potential energy (stored in the spring) and part kinetic energy.
When the spring is initially compressed, the payload is at rest, so all energy is elastic potential.
Once the spring has returned to its natural state, all this elastic potential energy must have been turned into kinetic energy.
If the payload is launched horizontally, and no gravity is present,this means that its final speed will be horizontal only also, according to Newton's First Law.
So, we can write the following equation:
where ΔU = -1/2*k*(Δx)² (2)
and ΔK = 1/2*m*v² (3)
Replacing in (2) and (3) by the givens, and simplifying, we can find the stiffness ks as follows: