Total Conceptual
A block slides down a frictionless ramp. Why does its mechanical energy stay the same? (Hint: What forces are doing work?)
No non-conservative forces (like friction) are doing work; only gravity, a conservative force, is involved.
In a U(x) = ½kx² graph, how do you know where the restoring force is strongest? (Hint: Force relates to slope!)
Where the slope (–dU/dx) is steepest; the force is largest in magnitude.
Define instantaneous power using force and velocity. (Hint: Use a dot product.)
P = Fv, the scalar (dot) product of force and velocity vectors.
A 10 N force moves an object 3 meters. How much work is done? (Hint: Use W = Fd.)
30 J
A person holds a heavy box still. Why is no work done? (Hint: Think physics, not effort.)
No displacement means zero work, even though muscles are active.
Under what condition will the work done by non-conservative forces be zero? (Hint: Think “idealized” systems.)
When non-conservative forces (like friction or air resistance) are absent or do no net work.
In a potential energy well, where is the net force zero? (Hint: Use the derivative of potential energy.)
Where the slope of U(x) is zero — at a local minimum or maximum.
A car engine provides constant power. What happens to its acceleration over time? (Hint: How does velocity affect acceleration?)
As velocity increases, acceleration decreases because P = Fv ⇒ a = P/(mv).
A 500 N/m spring is compressed 20 cm. What’s the max speed of a 1 kg object launched by it? (Hint: Convert PE to KE.)
Max speed = 4.47 m/s from 10 J = ½mv².
Can work be negative? (Hint: Think direction of force vs motion.)
Yes — if force opposes displacement, work is negative.
A spring is compressed twice as far. Does the object launched from it move four times faster? (Hint: Look at KE and spring energy.)
No. Spring potential energy x², so speed √x² = x. Doubling compression only doubles speed.
How can you tell whether motion is bound or unbound from a potential energy diagram? (Hint: Think about total energy lines.)
If total mechanical energy is below the peak of U(x), motion is bound. If it's above, motion is unbound.
How do you express instantaneous power of torque is changing over time? (Hint: Think angular versions of force and velocity.)
P(t) = τ(t) · ω(t), accounting for time-dependent torque.
A block compresses a spring and slides up a frictional ramp. What equation relates energy and work? (Hint: Total energy changes due to friction.)
ΔEmech=Wnc
ΔEmech = ΔK+ΔU
You land on a soft mat instead of concrete. Both stop you. Which did more work? (Hint: Compare energy transfer.)
Same work (ΔKE), but mat extends time, less force, safer.
A satellite orbits Earth in a perfect circle. How much work does gravity do? (Hint: Consider angle between force and motion.)
Zero work, because gravity is always perpendicular to the direction of motion.
What happens at turning points in a potential energy curve? (Hint: What happens to kinetic energy?)
Turning points are where kinetic energy = 0; the particle reverses direction where total energy equals U(x).
Two elevators lift the same mass the same height. One takes longer. Which used more power? (Hint: Work is the same—what varies?)
The one that lifts faster uses more power. P = W/Δt or P = Fv.
A rope pulls an object at an angle θ over distance d. What’s the work done? (Hint: Angle matters.)
W = T·d·cos(θ), where T is the tension.
“If potential energy decreases, kinetic energy must increase.” True or false? (Hint: What about friction?)
False. Non-conservative forces can reduce total mechanical energy.
A charged particle moves in a field with zero net work. What does that tell you about the net force? (Hint: What kind of motion would this imply?)
The net force is zero; no net force means no net acceleration, so no change in kinetic energy.
Why does a particle spend more time on one side of an asymmetric potential well? (Hint: Relate velocity to KE.)
The particle moves slower where KE is lower, so it spends more time there.
A vehicle’s engine must overcome air resistance. If F=bv², what is the max speed it can maintain with constant engine power? (Hint: P = Fv)
Terminal speed is v=^3 √ P/b
A variable force F(x) = ax² acts from x = 0 to x = L. Find the total work done. (Hint: Use integration.)
W=(aL^3)/3
“The normal force always does zero work.” True or false? (Hint: What if object is on a moving surface?)
False. Normal force can do work on curved or accelerating surfaces, but not when it’s perpendicular to displacement.