calculate the impulse imparted to the object in the following collision:
a 0.5 kg hockey puck moving a5 35 m/s hits a straw bale, stopping in 1 second.
a = Δv / Δt = 35 / 1 = 35 m/s^2
f = m a = 0.5 * 35 = 17.5 N
i = f t
To calculate the impulse imparted to the object in this collision, we can use the formula:
Impulse = Change in momentum = mass × change in velocity
Here's how we can apply the formula to the given scenario:
1. Calculate the initial momentum of the hockey puck:
Initial momentum = mass × initial velocity
Initial momentum = 0.5 kg × 35 m/s
2. Calculate the final momentum of the hockey puck:
Final momentum = mass × final velocity
Final velocity is 0 m/s because the hockey puck comes to a complete stop.
3. Calculate the change in momentum by subtracting the final momentum from the initial momentum:
Change in momentum = Final momentum - Initial momentum
4. Calculate the impulse:
Impulse = Change in momentum
Let's calculate the impulse:
Initial momentum = 0.5 kg × 35 m/s = 17.5 kg·m/s
Final momentum = 0.5 kg × 0 m/s = 0 kg·m/s
Change in momentum = Final momentum - Initial momentum
Change in momentum = 0 kg·m/s - 17.5 kg·m/s = -17.5 kg·m/s
Hence, the impulse imparted to the object in the collision is -17.5 kg·m/s. The negative sign indicates that the impulse is in the opposite direction of the initial velocity of the hockey puck.
To calculate the impulse imparted to the object in a collision, you can use the equation for impulse:
Impulse = Change in momentum
Momentum is defined as the product of mass and velocity:
Momentum = mass × velocity
In this case, we have a hockey puck with a mass of 0.5 kg moving at a velocity of 35 m/s. It hits a straw bale and stops in 1 second, which means the final velocity is 0 m/s.
First, let's calculate the initial momentum of the hockey puck:
Initial momentum = mass × initial velocity
Initial momentum = 0.5 kg × 35 m/s
Initial momentum = 17.5 kg·m/s
Next, let's calculate the final momentum of the hockey puck:
Final momentum = mass × final velocity
Final momentum = 0.5 kg × 0 m/s
Final momentum = 0 kg·m/s
Now, to calculate the change in momentum, we subtract the final momentum from the initial momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = 0 kg·m/s - 17.5 kg·m/s
Change in momentum = -17.5 kg·m/s
The impulse imparted to the object is equal to the absolute value of the change in momentum:
Impulse = | Change in momentum |
Impulse = | -17.5 kg·m/s |
Impulse = 17.5 kg·m/s
Therefore, the impulse imparted to the object in the collision is 17.5 kg·m/s.