Kinetic and gravitational potential stores
Calculate kinetic energy from mass and speed, and gravitational potential energy from mass, gravitational field strength and height. Use ideal drops and straight-up launches to find speeds and rise heights, with negligible resistance.
What a learner can do afterwards
- Calculates the kinetic store of a moving object and the gravitational store of a raised one
- Equates the two stores to find a landing speed or a rise height
- Explains why doubling speed makes kinetic energy four times larger when mass stays the same
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Kinetic energy KE = 0.5 × m × v². Use mass m in kilograms and speed v in metres per second to get joules. Square the speed before multiplying. At fixed mass, doubling speed multiplies KE by four. A same-car comparison at 60 mph and 30 mph uses a ratio; do not insert mph directly into this SI equation.
Near Earth's surface, gravitational potential energy GPE = mgh relative to a chosen zero height. Use mass in kilograms, height in metres and g in N/kg. Here choose the approximation g = 10 N/kg. A 0.4 kg object 5 m above the zero level has GPE = 0.4 × 10 × 5 = 20 J.
Drop that object from rest through 5 m, ignoring air resistance. Its 20 J loss of GPE equals its gain in KE. Thus 0.5 × 0.4 × v² = 20, so v² = 100 and v = 10 m/s just before impact. The energy balance uses the height lost, not the total length of a path.
For a straight-up launch, ignore air resistance and choose launch height as zero. At the highest point speed is zero, so launch KE equals gained GPE: 0.5mv² = mgh. Divide both sides by the same nonzero mass m: 0.5v² = gh. Then divide by g to get h = v² ÷ (2g). At 4 m/s with g = 10 N/kg, h = 16 ÷ 20 = 0.8 m.
Multiply both sides of KE = 0.5mv² by 2, then divide by mass: v² = 2KE ÷ m. Take the positive square root to undo squaring. For a 4 kg object with 50 J of KE, v² = 100 ÷ 4 = 25. Since 5 × 5 = 25, v = 5 m/s. Speed is nonnegative; do not stop at the squared-speed value.
Hold mass fixed when comparing speeds. A doubled speed gives 2² = 4 times the KE. At fixed speed, doubling mass only doubles KE. A comparison must say what stays unchanged. Ideal store swaps also require negligible resistance and no other energy transfers.
Half m v squared for motion, m g h for height, and falls swap one for the other.
Adapted from OpenStax College Physics explanations of kinetic energy, gravitational potential energy and conservation, openstax.org.
The rewritten readings were written for this dataset. Linked videos are from Khan Academy.
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