Collisions and Explosions Lab
Determination of the relationship between mass and final velocity for an explosion or collision
Purpose:
To determine the relationship between the mass of a cart and its final velocity for an “explosion” with another dynamics
cart of constant mass.
To verify the law of conservation of momentum in a collision between a moving cart and a stationary cart.
Theory:
The total momentum of the system should be conserved according to Newton’s third law of motion, in which the sum of
the initial momenta of the two objects (pA, pB ) is equal to their total momenta after the interaction (qA, qB):
pA + pB = qA + qB
(1)
mA uA + mB uB = mA vA + mB vB (2)
When two carts push against each other, they move apart such that the change in momentum of one object in one
direction is equal to the change of momentum of the other in the opposite direction.
∆pA = – ∆pB
(3)
mA (vA – uA) = – mB (vB – uB) (4)
For “explosions” in which the initial velocity of each of the two carts relative to each other is zero prior to the “explosion”,
then the formula (4) reduces to:
mA vA = – mB vB
(5) only when uA = uB = 0
So the velocity of each cart relative to the other cart is inversely proportional to its own mass. Therefore, if the mass of
the cart is doubled then the relative velocity of the cart should be reduced by half.
In this experiment, the mass of one cart (independent/manipulated variable) will be changed and the relative velocity
(dependent variable) of that cart will be determined by measuring the velocity of each cart. The velocity values will be the
maximum speed after the explosion which corresponds to the instant that the plunger breaks contact with the other cart
and is no longer providing an applied force and the cart stops speeding up (accelerating).
The same sensors, carts, and dynamics track will be used for all trials. The dynamics track will remain horizontal and
level, the spring-plunger will be compressed the same amount, and the mass of the other cart will remain constant for all
runs. The environmental conditions will remain relatively constant in the classroom and should not have a significant
effect on the results.
Procedure:
Setup SPARK or GLX Datalogger and PASPORT Motion Sensors
 Each station has two motion sensors set at narrow beam, angled horizontally, and connected an Xplorer GLX Datalogger
 The Xplorer GLX Datalogger shows the Velocity-Time graphs for both motion sensors, with a sample rate of 50 samples /s.
 Cart A is the red cart that will have extra masses added. Cart B is the blue cart that will have one 250-g mass added for all trials
 Press Play and move each cart to see which line corresponds to each cart.
“Explosions” Trial Runs
 Place the two carts near the center of the dynamics track so that the “loaded” plunger of one is in contact with the other cart.
 HOLD both carts in place against each other while holding down the plunger release button.
 Press Start on the GLX and then release the carts simultaneously.
 The changes in velocity and position should be seen in the graphs for each motion sensor.
 Record the maximum velocity of each cart immediately after the ‘explosion’.
 Add 0.25 kg to Cart A (red cart) then repeat the above procedure (Trial 2).
Collisions Trial Runs
 Place the cart B (blue cart) near the middle of the dynamics track.
 Press Start on the GLX and then roll the red cart (cart A) toward cart B..
 Record the maximum velocity of each cart immediately after impact.
 Add 0.50 kg to plastic Cart A then repeat the above procedure (Trial 2).
Table 1
Explosion Lab.
Effect of mass on final velocity and momentum in an explosion between dynamics carts.
The velocity of each cart before the “explosion” is zero, uA = uB = 0; The momentum of each cart is also zero, pA = pB = 0.
RED CART A – changing mass
Trial
mass added
m / kg
total mass,
mA / kg
1
0
0.25
2
0.25
0.50
3
0.50
0.75
4
0.75
1.00
maximum velocity after,
vA / m s-1
raw data from GLX
BLUE CART B – constant mass = 0.50 kg
momentum after,
qA / kg m s-1
calculated value
maximum velocity after,
vB / m s-1
raw data from GLX
momentum after,
qB / kg m s-1
calculated value
Absolute Error
Unbalanced Momentum
| qA + qB | / kg m s-1
 How well does your data support the equation: mA vA = – mB vB? (Show all calculations)
Table 2
Collision Lab.
mass
added
m / kg
total
mass
mA / kg
1
0
0.25
2
0.25
0.50
3
0.50
0.75
4
0.75
1.00
Trial
Final velocities of two carts after a moving cart (A) collides with a stationary cart (B). The positive direction is the initial direction of Cart A.
The velocity of blue cart B before the collision is zero, uB = 0. The momentum of B before the collision is zero, pB = 0
Mass of Cart A = 0.25 kg for all trials.
Mass of Cart B = 0.50 kg for all trials.
RED CART A – changing total mass
BEFORE IMPACT
AFTER IMPACT
maximum values
maximum values
velocity before
momentum before
velocity after
momentum after
uA / m s-1
pA / kg m s-1
vA / m s-1
qA / kg m s-1
raw data from GLX
calculated value
raw data from GLX
calculated value
BLUE CART B constant mass = 0.50 kg
AFTER IMPACT
maximum values
velocity after
momentum after
vA / m s-1
qA / kg m s-1
raw data from GLX
calculated value
Absolute Error
Momentum ‘Lost’
| qT – pT | / kg m s-1
 How well does your data support the equation: mA uA + mB uB = mA vA + mB vB? (Show all calculations)
 Create graphs that clearly demonstrates the relationship between the changing mass of one cart and the resulting absolute error in the total momentum of the
system for each type of interaction.
 Record all relevant observations that affect the precision or accuracy of the investigation.