1. Understand the Concepts
* Impulse: Impulse is the change in momentum of an object. It's calculated as the force applied multiplied by the time interval over which the force acts.
* Momentum: Momentum is the mass of an object multiplied by its velocity.
2. Identify the Given Information
* Mass of the ball (m) = 0.50 kg
* Initial velocity (v₁) = 0 m/s (at rest)
* Final velocity (v₂) = 3.1 m/s
* Force (F) = 235 N
3. Calculate the Change in Momentum
* Initial momentum (p₁) = m * v₁ = 0.50 kg * 0 m/s = 0 kg m/s
* Final momentum (p₂) = m * v₂ = 0.50 kg * 3.1 m/s = 1.55 kg m/s
* Change in momentum (Δp) = p₂ - p₁ = 1.55 kg m/s - 0 kg m/s = 1.55 kg m/s
4. Calculate the Time Interval
* Impulse (J) = Δp = 1.55 kg m/s
* J = F * Δt
* Δt = J / F = 1.55 kg m/s / 235 N = 0.0066 s
Answer: The mallet was in contact with the croquet ball for approximately 0.0066 seconds (or 6.6 milliseconds).
