Solving the Physics Problem: Finding Final Velocities of Spheres

In summary, The equation of restitution is used to calculate the final velocities of two objects after a collision. In this problem, the given coefficient of restitution is e=0.8 and the masses of the spheres are m1=2kg and m2=3kg. By setting up equations for conservation of momentum and using the given velocities, the final velocities can be
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Homework Statement


Given the figure below and knowing that the coefficient of restitution is e=0.8 find the final velocities of the spheres.


Homework Equations


m1v1 + m2v2 = m1v1' + m2v2'
e = v2' - v1'/v1 - v2


The Attempt at a Solution


I have tried this a bunch of different ways and am not getting the answer (va' = 18.2 ft/s, vb' = 6.57 ft/s).

I tried breaking the velocity of ball a up into components along the center axis and the axis perpendicular.

Va on the center axis = 18cos(40) = 13.79 ft/s

I then set up equations along the axis for conservation of momentum and COR:

(2/32.2)*13.79 + (3/32.2)*(-12) = (2/32.2)*Va' + (3/32.2)*Vb'

so Vb' = -2.807 - .667*Va'

Also:

e = (Vb' - Va')/(13.79 - (-12)) = 0.8 , after plugging in Vb' from above

I get Va' = -70.39 ft/s which is way off.

I have tried other methods also that are also wrong, some closer though.

I am just completely stuck now.
 

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My professor hasn't been much help either. I am at a loss as to where I am going wrong. Any help is greatly appreciated! m1=2kg | m2=3kg | | | | | v1=18 ft/s | | | | | v2= -12ft/s | | | | | | | |
 

FAQ: Solving the Physics Problem: Finding Final Velocities of Spheres

What is the formula for finding the final velocity of a sphere?

The formula for finding the final velocity of a sphere is Vf = Vi + at, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and t is the time taken.

How do you determine the initial and final velocities of a sphere?

The initial and final velocities of a sphere can be determined by measuring the displacement, time, and acceleration of the sphere using appropriate tools and formulas. Alternatively, they can also be calculated using the known mass and force acting on the sphere.

How does the shape and size of a sphere affect its final velocity?

The shape and size of a sphere do not have a direct impact on its final velocity. However, they can indirectly affect it by altering the air resistance and friction on the sphere's surface, which in turn can affect its acceleration and final velocity.

What are the units of measurement for final velocity in this problem?

The units of measurement for final velocity in this problem are typically meters per second (m/s). However, depending on the given values and equations, it may also be expressed in other units such as kilometers per hour (km/h) or miles per hour (mph).

How can you check the accuracy of your final velocity calculation?

The accuracy of the final velocity calculation can be checked by comparing it to the expected or theoretical value. This can be calculated using other known values, such as the displacement, time, and acceleration, using appropriate equations. Additionally, the calculation can also be checked by performing the experiment multiple times and averaging the results.

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