A toy launcher's spring is squeezed back at the base of a ramp, with a 0.5 kg ball resting against it.
The spring stores 9 J of elastic potential energy. Friction and air resistance are negligible.
The spring fires. The ball shoots across the flat and glides up the ramp until it stops for an instant. How fast does the ball leave the spring, and how high does it stop?
Take three snapshots: A, just before the spring fires; B, just after the ball leaves the spring; C, at the instant the ball stops on the ramp.
At A, all 9 J sit stored in the spring. The ball is at rest on the flat, so its kinetic energy is 0 J and its gravitational potential energy is 0 J.
Friction and air resistance are negligible here, so the total mechanical energy of the ball and spring stays constant: 9 J at every snapshot.
At B the spring has emptied, so the ball carries 9 J of kinetic energy. 2 × 9 = 18. 18 ÷ 0.5 = 36. The speed is the square root of 36: the ball leaves the spring at 6 m/s.
At C the ball is momentarily at rest, so all 9 J sit as gravitational potential energy.
Take g = 9.8 N/kg. 0.5 × 9.8 = 4.9. 9 ÷ 4.9 = 1.84. The ball stops about 1.84 m above the flat.
A chain can carry more snapshots, but every column of the account obeys the same rule: the three stores change, and their total does not.
A spring at the base of a frictionless ramp stores 9 J of elastic potential energy behind a 0.5 kg ball. The spring fires. Find the ball's speed as it leaves the spring, and the height where it momentarily stops on the ramp. Take g = 9.8 N/kg.
Write down the values in the question:
EPE at A = 9 J, m = 0.5 kg; v at B = ?, h at C = ?
Hold the total mechanical energy constant across the snapshots:
KE at B = 9 J, and GPE at C = 9 J
Solve for the speed at B:
2 × 9 = 18
18 ÷ 0.5 = 36
v = √36 = 6 m/s
Solve for the height at C:
0.5 × 9.8 = 4.9
9 ÷ 4.9 = 1.84
h ≈ 1.84 m
The ball leaves the spring at 6 m/s and stops about 1.84 m up the ramp.
A spring in a dart launcher stores 12.25 J of elastic potential energy behind a 0.5 kg dart on a frictionless track. The spring fires. Enter the dart's speed as it leaves the spring, in m/s.
A compressed spring stores 14.7 J of elastic potential energy behind a 1 kg block at the base of a frictionless ramp. The spring fires, and the block slides up the ramp until it momentarily stops. Take g = 9.8 N/kg. Enter the height where it stops, in m.
A spring launcher on the floor stores 5 J of elastic potential energy behind a 0.4 kg cart at the base of a smooth hill. The spring fires. Find the cart's speed on the flat, and its kinetic energy at a point 1 m up the hill. Take g = 9.8 N/kg.
Write down the values in the question:
EPE = 5 J, m = 0.4 kg; v on the flat = ?, KE at 1 m = ?
On the flat, all 5 J are kinetic energy.
2 × 5 = 10
10 ÷ 0.4 = 25
v = √25 = 5 m/s
At 1 m up the hill, find the gravitational potential energy first:
0.4 × 9.8 = 3.92
3.92 × 1 = 3.92
GPE = 3.92 J
5 - 3.92 = 1.08
KE = 1.08 J
The cart leaves the spring at 5 m/s and still carries 1.08 J of kinetic energy at the 1 m mark.
A spring fires a 0.5 kg puck from the base of a smooth ramp with 10 J of stored elastic potential energy. Take g = 9.8 N/kg. Enter the puck's kinetic energy at a point 0.8 m above the base, in J.
A launcher's spring stores 6.9 J of elastic potential energy behind a 0.4 kg ball at the base of a frictionless ramp. The spring fires, and the ball passes a mark 1.25 m above the base, still moving. Take g = 9.8 N/kg. Enter the ball's speed at the mark, in m/s. Answers within 2% are accepted.
A spring under a launch pad stores 6.125 J of elastic potential energy behind a 0.25 kg ball at the bottom of a smooth curved track. The spring fires, and the ball glides up the track until it momentarily stops. Take g = 9.8 N/kg. Enter the height where it stops, in m.
A spring fires a ball across a frictionless flat and up a ramp. Snapshot B is just after launch, on the flat; snapshot C is where the ball momentarily stops on the ramp. Between B and C, which energy transfer happens?