A 3kg ball is accelerated from rest to a speed of 10 m/s. What is the impulse?
force = change in momentum / change in time
so
force * time = change of momentum = impulse
m * v - m * 0 = 3 * 10 = 30 kg m/s
To find the impulse, we need to use the equation:
Impulse = change in momentum
The momentum of an object is given by the equation:
Momentum = mass * velocity
Given that the mass of the ball is 3 kg and it is accelerated to a speed of 10 m/s, we can calculate the change in momentum.
Initial momentum = mass * initial velocity
Initial momentum = 3 kg * 0 m/s
Initial momentum = 0 kg m/s
Final momentum = mass * final velocity
Final momentum = 3 kg * 10 m/s
Final momentum = 30 kg m/s
Change in momentum = Final momentum - Initial momentum
Change in momentum = 30 kg m/s - 0 kg m/s
Change in momentum = 30 kg m/s
Therefore, the impulse is 30 kg m/s.
To find the impulse, we need to use the formula:
Impulse = Change in momentum
The formula for momentum is:
Momentum = mass × velocity
So, first, we calculate the initial momentum (momentum before the acceleration) and the final momentum (momentum after the acceleration).
Given:
Mass of the ball (m) = 3 kg
Initial velocity (u) = 0 m/s (since the ball is at rest)
Final velocity (v) = 10 m/s
Initial momentum (p_initial) = mass × initial velocity
p_initial = 3 kg × 0 m/s = 0 kg·m/s
Final momentum (p_final) = mass × final velocity
p_final = 3 kg × 10 m/s = 30 kg·m/s
Now, we can find the change in momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = p_final - p_initial
Change in momentum = 30 kg·m/s - 0 kg·m/s = 30 kg·m/s
Therefore, the impulse is 30 kg·m/s.