Conservation Of Momentum

CONSERVATION OF MOMENTUM Sazliman Ismail Mahmud Ahmad Tho Siew Wei Norazlilah Md. Nordin

INTRODUCTION • Elastic and inelastic collisions are performed with two dynamics carts of different masses. Magnetic bumpers are used in the elastic collision and Velcro bumpers are used in the completely inelastic collision. In both cases, momentum is conserved. Cart velocities are recorded using two Rotary Motion Sensors connected to the carts.

INTRODUCTION • This measurement method adds very little friction to the experiment and, since the velocities are continuously monitored, any deceleration due to friction can be measured. The total kinetic energy before and after the collision is studied. Another twist on the example of a collision would be the idea of a reverse collision or an explosion. If you video tape an explosion and play it backwards, it looks like a collision. Likewise, if you video tape a collision and play it backwards it resembles an explosion.

INTRODUCTION • If we look at the case of a canon being fired, we find there is a force of the gun powder exploding creating a force of the canon pushing on the cannon ball and the cannon ball pushing back on the gun. These two forces are equal in size but opposite in direction. If any forces that are external to the cannon-&-ball system (such as weight and friction) are removed. Then momentum must be conserved.

THEORY • The momentum of a cart depends on its mass and velocity. Momentum = p = mv

• The direction of the momentum is the same as the direction of the velocity. • During a collision, the total momentum of the system of both carts is conserved because the net force on the system is zero. • This means that the total momentum just before the collision is equal to the total momentum just after the collision. • If the momentum of one cart decreases, the momentum of the other cart increases by the same amount. • The law of conservation of momentum is stated as pTotalBeforeCollision = pTotalAfterCollision

THEORY • The Principle of conservation of momentum states that “ The total momentum of a system is always fixed if there is no external force acting on the system” or • “ In any collision or interaction between two or more objects in an isolated system , the total momentum of the system will remain constant ; that is the total momentum before collision will be equal to the total momentum after the collision”

Types of collision There are two types of collision , that is (i) Inelastic collision (ii) Elastic collision

Inelastic collision •

In inelastic collision , after two objects moving with their respective velocities do collide, they stick together and move with a common velocity.

•

Based on The Principle Of Conservation Of Momentum, The total momentum = The total momentum before collision after collision

m1u1 + m2u2 = (m1 + m2 )v

Elastic collision •

In elastic collision , after two objects moving with their respective velocities do collide, those two objects will separate and move with different velocities.

•

Based on The Principle Of Conservation Of Momentum, The total momentum = The total momentum before collision after collision m1u1 + m2u2 = m1v1 + m2v2

Explosion •

In explosion, two objects are initially at rest and after explosion those two objects will separate and move in opposite directions.

• •

Based on The Principle Of Conservation Of Momentum, The total momentum = The total momentum before explosion after explosion m1(0) + m2 (0) = m1 (-v1) + m2 v2

Similarities between Inelastic Collision and Elastic Collision Similarities Total momentum is conserved Total energy is conserved Total mass is conserved

Differences between Inelastic Collision and Elastic Collision Inelastic collision

Elastic collision

Both objects stick together after collision and move with a common velocity

Both objects don’t stick together after collision and move with different velocities

Total amount of kinetic energy is not conserved

Total amount of kinetic energy is conserved

APPARATUS • 2 Motion sensor, 2 carts (250g), 2.2 m track, and laptop with DataStudio software.

SETUP • Level the track using the leveling screws on the track feet. Make sure a cart at rest on the track, it should not move.

SETUP • Plug the motion sensor to the both edge of the track.

SETUP • Connect the two sensor to the computer and run DataStudio on the computer.

PROCEDURES (Inelastic Collision) Friction-compensated Sensor Cart 1 Cart 2

PROCEDURES • • • • • •

The plane is inclined to compensate for friction so that the trolley will move down the plane with a constant velocity when given a slight push. The same mass carts are used with the Velcro sides toward each other so the carts will stick together. This is a totally inelastic collision. Click on START on the computer and Cart 2 at rest, Cart 1 has velocity toward Cart 2. Cart 1 and Cart 2 are moving toward each other with about the same speed (stick together). Then, click on STOP. The velocity vs. time graph is using on the computer, the velocity of cart 1 just before and after the collision is found.

DATA TABULATION

DATA ANALYSIS • Inelastic Collision Final velocity according to formula;

m1u1 + m2 u 2 = ( m1 + m2 ) v

(0.25)(0)+(0.25)(0.156) = (0.25+0.25)v 0.50v = 0.0390 v = 0.078 m/s Final velocity from the graph 1 (experiment); v = 0.080 m/s

PROCEDURES (Elastic Collision) Sensor

Sensor Cart 1

Cart 2

P1

P2 = 0

Sensor

Sensor Cart 1

Cart 2

P1

P2

PROCEDURES • •

• • • •

Two motion sensors are fixed at the both end. The same mass carts are used with one cart moving and one cart static (but no Velcro sides) toward each other so the carts will bounce off each other and the collision will be elastic. Click on START on the computer and Cart 2 at rest, Cart 1 has velocity toward Cart 2. Cart 1 and Cart 2 are moving toward each other with different velocity. Then, click on STOP. The velocity vs. time graph is using on the computer, the velocity of Cart 1 and Cart 2 just before and after the collision is found.

DATA TABULATION

DATA ANALYSIS • Elastic Collision Final velocity (second cart) according to formula;

m1u1 + m2 u 2 = m1v1 + m2 v 2

(0.25)(0)+(0.25)(0.58) = (0.25)(0.46) + (0.25)v2 0.115 + 0.25v2 = 0.145 v2 = 0.120 m/s Final velocity from the graph 2 (experiment); v = 0.100 m/s

DATA TABULATION

DATA ANALYSIS • Elastic Collision (two moving carts) Final velocity (second cart) according to formula;

m1u1 + m2 u 2 = m1v1 + m2 v 2

(0.25)(0.20)+(0.25)(0.70) = (0.25)(0.58) + (0.25)v2 0.145 + 0.25v2 = 0.225 v2 = 0.32 m/s Final velocity from the graph 3 (experiment); v = 0.28 m/s

PROCEDURES (Explosion) Plunger Sensor

Cart 1

Cart 2

Sensor

PROCEDURES • • • • •

The plunger on one cart is depressed. The two carts are placed on the track so that they are in contact with each other. Click on START on the computer and tap the trigger release to launch the carts. Click on STOP. The velocity vs. time graph is using on the computer. Also, it might be helpful to expand the graph, to see just that area you are interested in. The momentum of each cart after the explosion is calculated.

DATA TABULATION

DATA ANALYSIS • Explosion Final velocity (second cart) according to formula;

0 = m1v1 + m2 v 2

0 = (0.25)(0.30) + (0.25)(-v2) 0.25v2 = 0.075 v2 = 0.30 m/s Final velocity from the graph 4 (experiment); v = 0.30 m/s

DISCUSSION • The result for all the experiments show that there only a small error occurs when compared the value of experiment and from formula. For the first experiment the error just 2.56 %, second is 16.67 % and the third experiment is 12.50 %. The last experiment shows there is no different value for final velocity between experiment and formula. We all had concluded that the different may be caused by the plane is not totally compensated. There is still a friction between carts and plane.

RECOMMENDATION • These experiments had an element of fun and involved real scientific thinking. The probeware are easier to use because it is user-friendly. • We found their concepts of mechanics and motion were dramatically changed through activities incorporating probeware. • It was absolutely a completely new (and better) way to teach and learn Physics because it took a shorter time and the minimum error compared to the conventional apparatus.

RECOMMENDATION • The students could do experiments at first, collect realtime data using probeware, then offer explanations. • Basically, the students can construct their own knowledge in a structured, safe environment, with teachers act as a guide and facilitator. • We think the technology we've used in this experiment can inspired the students to seek professional qualifications such as engineering (mechanical, electrical and automotive). • The students will be exposed to a wide range of skills and equipment associated with the use of probeware.

PRECAUTION • • •

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All connections must be tight and secure. The trolleys must be in line of the lane. A friction- compensated runway is a runway which allows the trolley to move with uniform velocity. To make sure that the friction of the runway is compensated, modified the level of runway to make sure trolley moving with uniform velocity. Take a several readings of to get accurate results.