Impulse Lab

Introduction
In this week's lab we crashed an empty red cart into a force-probe with aluminum (to slow down time) attached to a ring stand. We found the velocity of the cart before and after the collision. We then found the change in momentum, also known as impulse. We did this to measure the relationship between impulse, force, and time during a collision.

cart with aluminum

force prob with aluminum

Key Info

• impulse: a change in momentum (another way of representing the conservation of momentum)
• impulse is measured in Joules

• momentum = P

• impulse equation: J = Pfinal - Pinitial

• mass of car: 0.25 kg

• velocity is measured in meters per second (m/s)

Big Question

What is the relationship between impulse, force, and time during a collision?

After we collided the car with the aluminum ring, we found the velocity of the cart in the collision before and after using the sonic range finders. Then we found the momentum before and the momentum after to find the impulse. Then we recorded the area, also known as the integral, under the Force vs. Time graph. 



Here is what our data looked like:

From here, we did the calculations and found that the area of a force vs. time graph is impulse. So now the equation for impulse can be written as Impulse = Force (Time) or J = F(t).

Analyzing Data

Concluding Ideas
       Impulse and Are are the same! After determining the area of a Force vs. Time graph and calculating the impulse, the answers come out to be equal. Forces are equal and opposite; therefore, the impulse remains constant in a collision by increasing the time and decreasing the force. In the collision, the metal sheets increased the time and decreased the force.

Real Life Connection
        Boxing uses this same principle of minimizing the effect of a force by extending the time of the collision. When a boxer recognizes that he will be hit in the head by his opponent, the boxer often relaxes his neck and allows his head to move backward upon impact. This known as "riding the punch." A boxer rides the punch in order to extend the time of impact of the glove with their head. Extending the time results in decreasing the force and then minimizing the effect of the force in the collision. Now that is physics in action!
  
Here's a clip from the final fighting scene in the movie Rocky Balboa 

Collisions Lab

The BIG Question
   
    What is the difference between the amount of energy lost in an elastic collision vs. inelastic collision?
    What is a better conserved quantity- momentum or energy?

Background

• scalar quantities: magnitude (mass, energy, temperature)
• vector quantities: magnitude and direction ( + rightward, - leftward)
• types of collisions:
• elastic- objects bounce off each other
• inelastic: objects stick together
• momentum: p = m (v)
• mass (velocity)
• mass is measured in kilograms (kg)
• velocity is measured in meters per second (m/s)

• In this week's lab, our goal was to find the difference between the amount of energy lost in an elastic collision and inelastic collision. To test this, we put two cars of the same mass on opposite sides of a track, one red and one blue. We set two range finders on the ends of the track, which measure the velocity of the cars. These range finders were plugged into the electronic force probe, which was then plugged into the computer. The application on the computer graphed the velocity of both cars before, during, and after the collision.

• For the inelastic collision, we pushed the red car to the right toward the blue car, which then stuck together with velcro. Both cars continued to move together to the right. 

• For the elastic collision, we pushed the red car with a spring toward the blue car to the right. In this collision, the red car followed the blue car at a much slower pace once they hit, while the blue car continued to move to the right.

• We recorded our data and found the total momentum (p = mv) and the total kinetic energy (KE = 1/2mv^2) of both collisions.

• Then we found the percent difference of both the amount of energy and momentum that left or entered the system for both elastic and inelastic collisions.

• Percent difference: 

• Kinetic energy: (Total after - Total before)/(Total after + Total before / 2) (100)

• Momentum: (Total after - Total before)/(Total after + Total before / 2) (100) 

• We found that momentum is a better conserved quantity rather than energy because more energy is given off during a collision. Momentum has a smaller percent difference.

• We also found that inelastic collisions lose more energy than elastic collisions

Real Life Connection: 

      The game of pool uses the exact same concepts of momentum in collisions. When the white ball hits another colored ball, the hit and the colored ball keeps moving. The goal of the game is to get all the colored balls in the holes without knocking the white ball in with them. The velocity of the balls plays a key part in strategizing.