A 200 kg luggage cart rolls at 3 m/s. Half the mass is 0.5 × 200 = 100, the speed squared is 3 × 3 = 9, and 100 × 9 = 900, so 900 J.
Load the same cart to double the mass, same speed. Does the energy quadruple the way it did for speed?
Run the count on the loaded cart: 400 kg at the same 3 m/s.
Half the mass is now 0.5 × 400 = 200, and 200 × 9 = 1800, so 1800 J.
The mass doubled, and the kinetic energy doubled: 900 J to 1800 J. No quadrupling.
The reason sits in the equation. The mass enters KE = ½mv² once, not squared.
An empty kayak carries 250 J of kinetic energy. With a passenger aboard its mass is double, and it moves at the same speed. Enter the loaded kayak's kinetic energy in J.
A 2 kg camera drone carries 22 J of kinetic energy at cruising speed. A 6 kg model flies at the same speed. Calculate the heavier drone's kinetic energy.
The mass is multiplied by 3, and the speed is unchanged.
The kinetic energy is multiplied by 3.
KE = 22 × 3 = 66
The heavier drone's kinetic energy is 66 J.
A loaded trailer carries 5400 J of kinetic energy. Unloaded, its mass halves, and it moves at the same speed. Calculate the unloaded trailer's kinetic energy.
The mass is multiplied by 0.5, and the speed is unchanged.
The kinetic energy is multiplied by 0.5.
KE = 5400 × 0.5 = 2700
The unloaded trailer's kinetic energy is 2700 J.
Set the two factors side by side. Speed enters squared: doubling it quadruples the KE. Mass enters once: doubling it doubles the KE.
Ugo says: 'A loaded dump truck with three times the mass of an empty one, moving at the same speed, carries three times the kinetic energy.' Is Ugo correct?
One scooter's mass doubles, speed unchanged. A second identical scooter's speed doubles, mass unchanged. Which change multiplies the scooter's kinetic energy by more?
A single light-rail car carries 8000 J of kinetic energy. Two identical light-rail cars coupled together move at that same speed. Enter the coupled pair's total kinetic energy in J.
Doubling a van's mass only doubles its kinetic energy, while doubling its speed quadruples it. Why the difference?
A delivery van's mass is multiplied by 4 while its speed stays the same. Its kinetic energy is multiplied by ___.