2.4c - Collisions and Explosions

Momentum Resources:

- - Kognity Online Textbook - Use your ACS Login
  - IB Physics Site - Comprehensive Notes
  - IB Physics Net - Comprehensive Notes
  - Topic 2 Flashcards - Vocab Practice
  - Khan Academy - Momentum/Impulse
  - The Physics Classroom

Energy Transfer and Conservation of Momentum

Pendulum Sweet Spot

A group of students wants to determine the height of a needs to be released to completely transfer its energy

Swing Pendulum and find the 'sweet spot' / 'threshold height'.
1. Determine the height Δy_t at which the bob of the pendulum is zero after the collision. (all momentum is transferred to the block)
2. Collect
  1. Δy - Release height
  2. x - slide distance
Find F_f of the block and surface
1. Using spring scale and Hooke's law, pull block at constant speed.
2. Draw FBD to illustrate the horizontal forces acting on the block.
Find ratio of Work out/Energy after collision (F_f • x) v. Work in/Energy before the collision (mgΔy)
1. Find percent energy loss in the collision
Challenge:
1. For a given Δy (Δy_g), predict x, where Δy_g > Δy_t

Ballistic Pendulum

A ballistic pendulum is a device that could be used by a crime-scene investigator to determine the muzzle velocity of a gun. The bullet comes out of the gun at high speed, and embeds itself into a target that is hanging from a string. This causes the target (with the bullet embedded) to swing back and forth, pendulum style. By knowing the maximum height that the target reaches, the speed of the bullet can be determined.

Ballistic PendulumA ballistic pendulum is demonstrated and a full solution is worked out including real numbers and variable comparisons.

NASA DART Mission

NASA's First Planetary Defense Test Missiondart.jhuapl.edu/

The Physics of Smashing a Spacecraft Into an AsteroidNASA will soon release the results of its DART mission to find out whether crashing a probe into a space rock can deflect it. Here’s how they'll do the math.

The Double Asteroid Redirection Test (DART): Planetary Defense Investigations and Requirements

Why NASA smacked an asteroidDid the DART mission work??If you enjoy space videos, I made a longer one about how the JWST found water here: https://youtu.be/ampB1laCWF4 And if you like m...

NASA Confirms DART Mission Impact Changed Asteroid’s Motion in SpaceAnalysis of data obtained over the past two weeks by NASA’s Double Asteroid Redirection Test (DART) investigation team shows the spacecraft's kinetic impact with its target asteroid, Dimorphos, successfully altered the asteroid’s orbit. This marks humanity’s first time purposely changing the motion of a celestial object and the first full-scale dem

Data:

Mass of Dimorphos [M] = 5 x 109 kg
Velocity of Dimorphos = 0 m/s (as a relative measurement)
Mass of DART = 610 kg
Velocity of DART = 6.3 km/s (relative to Dimorphos)
Angle of impact 90˚

Using the data above and assuming an inelastic collisions, determine the change in velocity of Dimorphos.

When a push becomes a collision...

Momentum and You

Collisions

Scenario #1: Equal Masses - One at rest (p=0kgm/s)

A 2kg red-cart mass is traveling to the right (+) at 2m/s. It collides with a stationary 2kg blue-cart of the same mass. The collision is perfectly elastic. The momentum of red-cart is completely transferred to the blue cart. The red cart comes to a stop and the blue cart moves to the right at +2.0 m/s.

The incoming object comest to a stop and the target gains the exact speed as the incoming object. This is often seen in the game of pool when the cue ball strikes another ball.

Scenario #2: Equal Masses - Opposite Velocities

A 2-kg red cart is traveling to the right at +2.0m/s. It collides an identical blue cart traveling in the opposite direction. Both carts bounce elastically off of each other. This results in a 'swapping' of momentum, causing the two carts to bounce back with the same speed but opposite direction as before the collision.

When the two interacting objects meet, they have equal and opposite momenta (pl of momentum). In the scenario shown the two objects are identical, with equal masses and opposite velocities, so they also have equal and opposite momenta. However, this scenario also holds when the objects only have opposite momenta, they simply swap velocities.

Scenario #3: Large Mass into Light Mass at Rest

This type of collision is often seen in videos on YouTube. When a large moving object collides with a small object at rest the smaller object flies forward at a high velocity.

This is also the basis for many sports that we play. Hitting a golf ball is an excellent example. Notice the club does not slow, however the ball leaves at a high rate of speed. This video also demonstrates the importance of following through on a shot as it will increase the time the force (club) is in contact with ball. (F t = m ∆v.) This also the basis for kicking any sort of ball.

A 3kg red cart is traveling to the right with a velocity of +2m/s, giving it a total of 6kgm/s of momentum. It collides with a much smaller mass of 0.2kg that is at rest. Following the collision, the velocity of the 3kg mass is reduced to +1.75m/s. This causes the smaller 0.2kg mass to move with a velocity of 3.75m/s. The momentum is conserved as the sum of the momentum of the two carts remains 6kgm/s.

Scenario #4: Light Mass into Large Mass at rest

Often the large object remains at rest and the smaller object simply bounces off with an opposite momentum. In the scenario shown the difference in mass is 15x, however the large mass does move. We can think of the Earth as Mass_2 when we are bouncing on it.

The Great Escape (1963)

In the case of an object bouncing off a larger mass, a relatively small mass of 0.2kg bounces off a larger mass of 3kg. In a perfectly elastic collision, the larger mass does move, however in reality this motion may be undetectable. If a 0.2kg red cart traveling at 2m/s collides with a stationary 3kg mass. The red cart will rebound with a velocity of -1.75 m/s causing the blue cart to move with a velocity of +0.25m/s.

Conservation of Momentum Problems

Scenario #1: Opposite direction, similar velocities

Suppose two objects are approaching each other and collide. After colliding they stick together. Mass_1 is 4 kg and has a positive velocity of 4 m/s. Mass_2 is also 4 kg but has a velocity of -6m/s (moving to the left). In our diagram below, Mass_1 is red and Mass_2 is blue.

The horizontal axis represents the mass of the object while the y-axis represents the velocity of the object. Objects moving to the right or upwards are positive, while objects moving leftwards or downwards are negative. If an object has a velocity of 0 m/s, the velocity js shown as a bar. The AREA of each square or rectangle represents the momentum of each object. The sum of the two rectangles is equal to the total momentum. This total value does not change.

We want to determine v_f

substituting in the values of the two objects:

this equals the p_after (p_2)

substitute the after values

Solve for v_f

velocity of final two masses:

Scenario #2: Equal masses, one stationary

In the second scenario, cart with a mass of 2kg is traveling at 4 m/s. It collides and sticks to a STATIONARY (v = 0 m/s) cart of mass 2kg. The momentum (p) before the collision is 8 kgm/s.

Momentum is conserved (always), the mass of the 2 cart system is now 4 kg. Combined these carts will travel to the right with a velocity of +2m/s.

This can be summarized in the equation above and solved in the same way as above.

Can you show that the v_f of scenario #2 is 2m/s?

Level One Problems

Make a copy of the document above.
Solutions - PDF

Please make a copy of the diagram above if you would like to save the image.

Types of Collisions

Momentum is conserved, but what about energy

Your group will be given one of the following collisions:

Magnetic repulsion
Spring Bounce
Clay Cones
Velcro

By measuring the velocities of the carts before and after the collisions, determine the loss of energy in your given collision.

Launch cart 1 with constant energy (energy in compressed spring).

Vary the masses of cart 1 and/or cart 2.

Types of Collisions Data Collection

Collisions Data

Assigned thru GC.

Bouncing Collisions Data Table - Effect of Mass

Sticking Collisions Data Table - Effect of Mass

In the data table, only the white (blank) cells should be filled with measurements taken directly from Graphical Analysis.

All colored cells should be calculations.

Complete the data collection in the spreadsheet provided in GC.

For each run, determine the momentum (mv) of each cart before the collision, after the collision, and the total momentum before and after the collision. Calculate the ratio of the total momentum after the collision to the total momentum before the collision. Enter the values in Table 3.
For each run, determine the kinetic energy (KE = ½mv2) for each cart before and after the collision. Calculate the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision. Enter the values in Table 4.
If the total momentum for a system is the same before and after the collision, we say that momentum is conserved. If momentum were conserved, what would be the ratio of the total momentum after the collision to the total momentum before the collision?
If the total kinetic energy for a system is the same before and after the collision, we say that kinetic energy is conserved. If kinetic energy were conserved, what would be the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision?
Inspect the momentum ratios in Table 3. Even if momentum is conserved for a given collision, the measured values may not be exactly the same before and after due to measurement uncertainty. The ratio should be close to one, however. Is momentum conserved in your collisions?
Repeat the preceding question for the case of kinetic energy, using the kinetic energy ratios in Table 4. Is kinetic energy conserved in the magnetic bumper collisions? How about the hook-and-pile collisions? Is kinetic energy conserved in the third type of collision? Classify the three collision types as elastic, inelastic, or completely inelastic.