ASVAB (Armed Services Vocational Aptitude Battery)Mechanical Comprehension (MC)Hard
A child is playing with a toy car that rolls down a frictionless ramp and then moves across a horizontal surface. If the car starts from rest at a height of 0.5 meters on the ramp and has a mass of 0.1 kg, what is its speed when it reaches the bottom of the ramp?
- A2.2 m/s
- B1 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 of the ramp, all energy is potential energy (PE = mgh). At the bottom, all potential energy is converted to kinetic energy (KE = 0.5mv²). So, mgh = 0.5mv². The mass (m) cancels out. v² = 2gh. v = √(2gh). Given h = 0.5 m and g = 9.8 m/s², v = √(2 × 9.8 m/s² × 0.5 m) = √(9.8) ≈ 3.13 m/s.
Why the other options are wrong
- A. This is incorrect; it's a common miscalculation, possibly using g=10 and then dividing by 2.
- B. This is too low; it might be a result of an incorrect formula or calculation.
- C. This is the value of g, not the speed of the car.
Conservation of Mechanical Energy (Gravity)
In the absence of non-conservative forces (like friction), the total mechanical energy (potential energy + kinetic energy) of a system remains constant. Gravitational potential energy is converted into kinetic energy, and vice-versa.
- PE_initial + KE_initial = PE_final + KE_final.
- For falling objects: mgh_initial = 0.5mv_final² (if starting from rest).
- Assumes no energy loss to heat, sound, etc.
Memory trick: Energy's never lost, just 'switches' its 'cost' – 'potential' to 'kinetic' it goes.