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Question: Please provide data of 4 diferent masses and the c...
Please provide data of 4 diferent masses and the calculations used
1. Objective
This lab will use objects on a smooth ramp with varying mass impacting a second object and measure the corresponding initial and final energy and momentum values.
A. Critical Concepts
A.i. Energy Conservation
A.ii. Momentum Conservation.
B. Methods
B.i. Elastic collisions
B.ii. Velocity measurements
B.iii. Calibrated masses
C. Tools
C.i. A smooth rigid surface about 1m long that can be tilted to form a ramp.
C.ii. Four objects of known mass. Two items should be identical (golf balls for example), one item lighter than those two, and one item heavier than those two.[1]
C.iii. Time recording device (such as stop watch or smart phone app) to measure short time intervals. Note you can also use a smart phone video recording device as a means to measure time if you can inspect each frame (in Logger Pro, for example) and know the rate of recording (frames per second).
2. Procedure
Follow the following steps to collect the data and calculate the indicated values
A. Set up the ramp in an open area where moving objects won't cause any damage. Prop up one end so you have an inclination between 10 and 20 degrees. Allow 2 to 3 meters clearance beyond the bottom of the ramp. (Try to avoid a large “step” at the bottom of the ramp by either adding a transition piece or butting up against the bottom edge material of the same thickness.) In the landing area you will want to mark graduated distances from the bottom of ramp in 0.5 m increments.
B. Measure and record the mass of each object. You may use a kitchen scale, fishing scale or similar device to determine their weight. Be as accurate as possible.
C. Select one of the items of similar mass. Place it near the top of the ramp from where you will release it to move freely to the bottom of ramp and mark the location on the ramp. Measure the height from the surface of the ramp at the release point to the level surface at the end of the ramp. Record this vertical height.
D. Release the object from the position near the top of the ramp and use your time measurement device to record the time to traverse 0.5m or 1.0 m. If possible, record time to traverse all 0.5m increments along the horizontal.
E. Use the time measurements and distances to calculate the objects velocity along the horizontal surface. Then use the objects mass to calculate the momentum and the total kinetic energy. (If your object is rolling, be sure to calculate the rotational energy, show that calculation, and include that in the total kinetic energy calculation.) Tabulate your results.
F. Compare the total kinetic energy with the potential energy change calculated with the mass and height of the ramp.
G. Place the second item of identical mass at the bottom of the ramp so that when the original item is released, it fully descends the ramp and then strikes the second item. Measure the resultant velocity of the second item after the collision and repeat this 3 or more times. Compare the resultant momentum and total kinetic energy with the momentum and total kinetic energy of the first item as measured in E above.
H. Repeat the measurements and analysis outlined in step “G” replacing the bottom item with the items of lower and higher mass respectively. Tabulate all your results.
3. Analyses
Write the governing equations that describe the energy of the projectile object and the target objects before and after the collision.
Describe qualitatively how the target object motion depends on the mass of the projectile and target objects.
What happens when the objects of equal mass collide? Explain.
How does the increase in mass of the target change the motion of the projectile after the collision? Explain.
[1]
Items may be round or not, but they must move freely on the ramp and horizontal surface. They should also be roughly the same size as this laboratory involves collisions and you will have clearer results if the points of impact are nearly aligned with the objects center of mass.
Explanation / Answer
IN the above problem,
Let the measured height of the projectile initially be h
then potential energy of the projectile mass in the begenning = KE of the projectile at the bottom of the ramp = mgh ( where m is the mass of the projectile)
The target objet, has 0 energy before the collision
after the collision, energy of the projectile is less than mgh, and the target mass has new velocity which gives it non zero kinetic energy, also sum of the final kinetic energies of these tywo objects must be equal to the initial potential energy of the projectile mass in accordance to consevation of energy for an elastic collision
so, initial hieght of projectile of mass M = h
initial PE = Mgh
when this reaches bottom of the plank, velocity of the projectile = u
but 0.5Mu^2 = Mgh
u = sqroot(2gh) .. (1)
After collision
let velocity of mass m be v and that of mass M be V
so from conservation of momentum
Mu = MV + mv
V = (Mu-mv)/M = (u - mv/M) = (sqroot(2gh) - mv/M)
also, from conservation of energy for elastic collisions
Mgh = 0.5MV^2 + 0.5mv^2
Mgh = 0.5M(sqroot(2gh) - mv/M)^2 + 0.5mv^2
solve for v to find final velocity of the mass m and use this to find V
So, if mass of projectile is higher, ithas high KE before impact and hence the target object gains more velocity upon impact. Hence, the target object recieves more velocity upon impact if projectile mass is high and target mass is low
When two objects of equal mass collide
the projectile mass comes to a rest after transferring itsvelocity to target mass
Increase in mass of target decreases the velocity imparted to the target mass as the momentum imparted to it remains the same but due too higher mass this momentum is translated to a lower value of velocity
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