ASVAB (Armed Services Vocational Aptitude Battery)Mechanical Comprehension (MC)Medium
A small toy car is released from rest at the top of a frictionless ramp. If the ramp is 0.5 meters high, what will be the car's speed at the bottom of the ramp?
- A1.0 m/s
- B4.9 m/s
- C9.8 m/s
- D3.13 m/s
Show answer & explanationAnswer & explanation
Correct answer: D. 3.13 m/s
This problem involves the conservation of mechanical energy. At the top, the car has potential energy (PE = mgh). At the bottom, it has kinetic energy (KE = 1/2 mv²). Since the ramp is frictionless, PE_top = KE_bottom. So, mgh = 1/2 mv². The mass (m) cancels out, leaving gh = 1/2 v². Solving for v: v = √(2gh). Using g ≈ 9.8 m/s² and h = 0.5 m, v = √(2 × 9.8 m/s² × 0.5 m) = √(9.8) m/s ≈ 3.13 m/s.
Why the other options are wrong
- A. Incorrect, likely a calculation error.
- B. Incorrect, this would be if v = gh, or if h was higher.
- C. Incorrect, this is g, not the velocity.
Conservation of Mechanical Energy
In the absence of non-conservative forces (like friction or air resistance), the total mechanical energy (sum of potential and kinetic energy) of a system remains constant.
- PE + KE = Constant.
- Potential energy converts to kinetic energy and vice-versa.
- Often used to solve problems involving objects moving under gravity.
Memory trick: What goes up as potential, comes down as kinetic.