In the experiment shown above, you are testing the \"elasticity\" of a collision
ID: 1494449 • Letter: I
Question
In the experiment shown above, you are testing the "elasticity" of a collision between two metal spheres. One sphere with mass 0.7 kg is attached to a string (assume the string is massless and of constant length), forming a pendulum. The second sphere with mass 0.2 kg is placed at the edge of a table of height 0.8 m. When the first sphere is hanging straight down, it just touches the second sphere and is right above the table.
To run the experiment, you pull back the pendulum until the first sphere is a height 0.60 m above the table. You release the pendulum, the first sphere swings down and collides with the second sphere. You then measure how far from the table the second sphere lands on the ground, xf.
If the collision between the spheres is totally elastic, where would the second sphere land, xf?
Give your answer in meters to at least three digits. Do not include the units in your answer.
Explanation / Answer
Energy is conserved during elastic collisions.
Step 1 Finding the energy of the blue sphere when it hits the red one.
Energy of the blue sphere = Mgh
It is pulled to a height of 0.6 m and released. The potential energy is converted into its kinetic energy,
E1 = 0.7 x 9.8 x 0.6
= 4.116 J
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Step 2 Equating the energies
Energy of the blue sphere = Energy of the red sphere
The energy of the red sphere = 1/2 mv2
Equating energies,
4.116 = 0.5 x 0.2 x v2
v2 = 41.16
v = sqrt(41.16)
= 6.416 m/s
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Step 3 Finding xf
Using the equation, H = 1/2gt2
time taken by the sphere to touch the ground, t = sqrt[2H/g]
= sqrt[(2 x 0.8) / 9.8]
= 0.404 s
Distance, xf = velocity x time
= 6.416 x 0.404
= 2.59 m