A 3 kg ball is in mid-flight above a practice court: 2 m up, moving at 4 m/s.
How much mechanical energy does it hold at that instant?
Well, count each store on its own. Moving at 4 m/s, the ball's kinetic energy is (0.5 × 3) × (4 × 4), which is 24 J.
Take g = 9.8 N/kg. At 2 m, the gravitational store is mgh: (3 × 9.8) × 2, which is 58.8 J.
No spring touches the ball, so its elastic store is 0 J.
Add the stores: 24 + 58.8 = 82.8, so the ball's mechanical energy at that instant is 82.8 J.
One instant, one column: list KE, GPE and EPE for that frozen moment and sum them. The conservation lessons will set two such columns side by side.
A 3 kg ball is 2 m above the court, moving at 4 m/s. Take g = 9.8 N/kg. Calculate its mechanical energy.
Write down the values:
m = 3 kg, v = 4 m/s, h = 2 m, g = 9.8 N/kg, ME = ?
Write down the equation:
ME = KE + GPE + EPE
The stores: KE is (0.5 × 3) × (4 × 4), which is 24 J; GPE is (3 × 9.8) × 2, which is 58.8 J; EPE is 0 J.
Substitute in the values, and calculate:
ME = 24 + 58.8 = 82.8
The ball's mechanical energy is 82.8 J.
A 4 kg cart rolls at 5 m/s along a shelf track 3 m above the floor. Take g = 9.8 N/kg, with the floor as h = 0. Enter the cart's mechanical energy in J.
A 1.2 kg drone flies at 5 m/s, 10 m above the ground. Take g = 9.8 N/kg, with the ground as h = 0. Enter the drone's mechanical energy in J.
In the same gym, a 1.5 kg ball rests on a launcher whose compressed spring stores 30 J. The ball sits 1 m above the floor. Take g = 9.8 N/kg. Calculate the ball's mechanical energy.
Write down the values:
m = 1.5 kg, v = 0 m/s, h = 1 m, EPE = 30 J, g = 9.8 N/kg, ME = ?
Write down the equation:
ME = KE + GPE + EPE
The stores: KE is 0 J; GPE is (1.5 × 9.8) × 1, which is 14.7 J; EPE is the given 30 J.
Substitute in the values, and calculate:
ME = 14.7 + 30 = 44.7
The resting ball's mechanical energy is 44.7 J.
A 0.1 kg dart moves at 4 m/s at floor level, still touching a launcher spring that holds 2 J. Take the floor as h = 0. Enter the mechanical energy of the dart-and-spring system at that instant in J.
A 5 kg toolbox rides a lift platform, moving at 2 m/s while 4 m above the ground. Take g = 9.8 N/kg, with the ground as h = 0. Enter the toolbox's mechanical energy in J.
A 0.5 kg ball is 4 m above the yard, moving at 6 m/s. Take g = 9.8 N/kg, with the yard as h = 0. Enter the ball's mechanical energy in J.
A 0.8 kg cart sits at rest against a compressed launcher spring that stores 12 J, on a ledge 2.5 m above the floor. Take g = 9.8 N/kg, with the floor as h = 0. Enter the cart's mechanical energy at that instant in J.