A pickup truck is carrying a 10.0 kg toolbox, but the tailgate of the truck is missing, so the box can slide out if it starts mo
ving. The coefficients of static and kinetic friction between the toolbox and the truck bed are 0.31 and 0.18, respectively. Assume that the truck bed is horizontal. What is the shortest time the truck could take to accelerate from rest to 13.2 m/s without causing the toolbox to slide
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Answer:
It must be 4 times high.
Explanation:
- Assuming that the car can be treated as a point mass, and that the ramp is frictionless, the total mechanical energy must be conserved.
- This means, that at any time, the following must be true:
- ΔK (change in kinetic energy) = ΔU (change in gravitational potential energy)
⇒
- Let's call v₁, to the final speed of the car, and h₁ to the height of the ramp.
So, at the bottom of the ramp, all the gravitational potential energy
must be equal to the kinetic energy of the car (Defining the bottom of
the ramp as our zero reference for the gravitational potential energy):
(1)
- Now, let's do v₂ = 2* v₁
- Replacing in (1) we get:
(2)
- Dividing (2) by (1), and rearranging terms, we get:
- h₂ = 4* h₁