A 10-g bullet is shot vertically into a stationary 8-kg block. The block lifts upward 3.0 mm. The bullet penetrates the block in a time of .001 seconds. Assume the force exerted on the block is constant. What is the impulse imparted on the block by the bullet?
1.5 N
To calculate the impulse imparted on the block by the bullet, we need to find the change in momentum of the block. Impulse is defined as the change in momentum, and can be calculated using the formula:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = Mass x Velocity
Since we know the bullet's mass and the time it takes to penetrate the block, we can find the bullet's velocity using the equation of motion:
Velocity = Distance / Time
First, let's calculate the velocity of the bullet:
Given:
Mass of the bullet (m1) = 10 g = 10/1000 kg = 0.01 kg
Time taken (t) = 0.001 seconds
The velocity of the bullet can be obtained by dividing the distance it penetrates the block by the time taken:
Distance = 3.0 mm = 3.0/1000 m = 0.003 m
Velocity = Distance / Time = 0.003 m / 0.001 s = 3 m/s
Now that we have the velocity of the bullet, let's calculate the momentum of the bullet:
Momentum of the bullet (p1) = Mass x Velocity = 0.01 kg x 3 m/s = 0.03 kg·m/s
The bullet imparts an equal and opposite change in momentum on the block, so the change in momentum of the block is:
Change in momentum of the block (Δp2) = -Change in momentum of the bullet (Δp1) = -0.03 kg·m/s
Hence, the impulse imparted on the block by the bullet is:
Impulse = Change in Momentum = -0.03 kg·m/s
Therefore, the impulse imparted on the block by the bullet is -0.03 kg·m/s.