what impulse is needed to slow a 45kg object from 15m/s to 12m/s?
To find the impulse needed to slow down an object, we can use the principle of impulse-momentum, which states that the impulse applied to an object is equal to the change in its momentum.
The formula for impulse is:
Impulse = Change in momentum
The momentum of an object can be calculated using the formula:
Momentum = Mass * Velocity
Given:
Mass (m) = 45 kg
Initial velocity (u) = 15 m/s
Final velocity (v) = 12 m/s
First, let's calculate the initial momentum (p₁):
p₁ = m * u
p₁ = 45 kg * 15 m/s
Next, calculate the final momentum (p₂):
p₂ = m * v
p₂ = 45 kg * 12 m/s
Then, find the change in momentum (Δp):
Δp = p₂ - p₁
Now, substitute the calculated values:
Δp = (45 kg * 12 m/s) - (45 kg * 15 m/s)
Δp = 540 kg·m/s - 675 kg·m/s
Finally, we can determine the impulse (J):
Impulse (J) = Δp
Impulse (J) = -135 kg·m/s
Therefore, the impulse needed to slow down the 45 kg object from 15 m/s to 12 m/s is -135 kg·m/s. The negative sign indicates a decrease in momentum.