Haruki works with F = ma. Wilma works with F = Δp/Δt. They study the same cart.
Do the two forms ever disagree? Run one case through both.
Take a 2 kg cart accelerating at 3 m/s².
The dynamics route: F = ma = 2 × 3 = 6 N.
Now the momentum route, over any stretch of time you like. Take 4 s.
In 4 s, the velocity grows by Δv = 3 × 4 = 12 m/s.
So the momentum grows by Δp = mΔv = 2 × 12 = 24 kg·m/s.
F = Δp/Δt = 24/4 = 6 N. The same 6 N.
That agreement is no accident. When the mass is constant, Δp = mΔv.
Divide by the time: Δp/Δt = m(Δv/Δt). And Δv/Δt is the acceleration, a.
So Δp/Δt = ma, and the two forms are one law.
A 2 kg cart accelerates at 3 m/s². Use F = ma to calculate the net force on it.
Write down the values:
m = 2 kg, a = 3 m/s², F = ?
Write down the equation:
F = ma
Substitute in the values, and calculate:
F = 2 × 3 = 6
The net force is 6 N.
The same cart, by the momentum route: over 4 s, its momentum rises by 24 kg·m/s. Use F = Δp/Δt to calculate the net force.
Write down the values:
Δp = 24 kg·m/s, Δt = 4 s, F = ?
Write down the equation:
F = Δp/Δt
Substitute in the values, and calculate:
F = 24/4 = 6
The net force is 6 N: the same prediction, from the same law.
A 3 kg cart accelerates at 5 m/s². Use F = ma. Enter the net force on it in N.
The same 3 kg cart, timed for 4 s: its velocity rises by 20 m/s, so its momentum rises by 60 kg·m/s. Use F = Δp/Δt. Enter the net force in N.
When do F = Δp/Δt and F = ma make the same prediction?
For a cart of constant mass, the two forms of Newton's second law give the same net force. What is the reason?
A 5 kg cart under a steady net force speeds up from 2 m/s to 8 m/s in 3 s. Use F = Δp/Δt. Enter the net force in N.
Haruki computes a cart's net force with F = ma. Wilma computes the same cart's net force with F = Δp/Δt. The cart's mass is constant. Which statement is correct?