THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Mechanical energy conservation
Does a longer smooth track mean a slower finish?
A small bead enters a fixed smooth track at 4 m/s. The exit is 2.4 m vertically below the entrance. The bead stays in contact with the track, which has no moving parts. Take g = 10 m/s².
What is its speed at the exit?
Organize the givens & assumptions
- Initial speed: 4 m/s
- Vertical drop: 2.4 m
- Gravity: 10 m/s²
Treat the bead as a particle. Ignore air drag and friction. The fixed track exerts a normal force perpendicular to the instantaneous motion.
Study with a tutor prompt
Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.
Opening this prompt marks this practice attempt as assisted.
Problem: Does a longer smooth track mean a slower finish?
A small bead enters a fixed smooth track at 4 m/s. The exit is 2.4 m vertically below the entrance. The bead stays in contact with the track, which has no moving parts. Take g = 10 m/s².
Question: What is its speed at the exit?
Givens:
- Initial speed: 4 m/s
- Vertical drop: 2.4 m
- Gravity: 10 m/s²
Assumptions: Treat the bead as a particle. Ignore air drag and friction. The fixed track exerts a normal force perpendicular to the instantaneous motion.
Choices (LaTeX):
A. 4\ \mathrm{m\,s^{-1}}
B. \sqrt{48}\ \mathrm{m\,s^{-1}}
C. 8\ \mathrm{m\,s^{-1}}
D. 28\ \mathrm{m\,s^{-1}}
Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.
Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.Start with the smallest hint.
Work through it with me.
One decision at a time. Pause, predict, then unpack the algebra.
Gravity remembers the change in height, not the length of the path.
Choose the energy zero
Put zero gravitational potential energy at the exit. At the entrance the height is +2.4 m.
Why is this step valid?
Only a potential-energy difference affects the answer; choosing the exit as zero simplifies the calculation.
Write the energy balance
The normal force does no work and there is no dissipation.
Why is this step valid?
The track redirects motion but does not add or remove mechanical energy.
Solve before substituting
Cancel the nonzero mass and multiply by two.
Why is this step valid?
Both terms have units m²/s². The mass cancels because both kinetic and gravitational energies scale with it.
Recover a speed
Speed is nonnegative, so take the positive square root.
Why is this step valid?
The energy equation gives a magnitude, not the final direction along the track.
The kinetic energy per kilogram increases from 8 J/kg to 32 J/kg. The increase is 24 J/kg, exactly gΔh.
TRY THE IDEA AGAIN
With the same start speed and endpoints, a longer smooth track gives…
YOUR LEARNING NOTE
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