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NemiM [27]
3 years ago
12

A simple pendulum of length 2.5 m makes 5.0 complete swings in 16 s. What is the acceleration of gravity at the location?

Physics
1 answer:
Norma-Jean [14]3 years ago
8 0
<h2>The acceleration of gravity at the location is 9.64 m/s²</h2>

Explanation:

Length of pendulum = 2.5 m

Time taken for 5 swings = 16 seconds

Time taken for 1 swing = 3.2 seconds

Period of pendulum = 3.2 seconds.

We have equation for period of simple pendulum as

             T=2\pi \sqrt{\frac{l}{g}}

Where l is the length of pendulum and g is acceleration due to gravity.

Substituting

                 T=2\pi \sqrt{\frac{l}{g}}\\\\3.2=2\pi \sqrt{\frac{2.5}{g}}\\\\g=\frac{4\pi^2 \times 2.5}{3.2^2}\\\\g=9.64m/s^2

The acceleration of gravity at the location is 9.64 m/s²

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There are some information missing on Part D: Let the mass of object 1 be m and the mass of object 2 be 3m. If the collision is perfectly inelastic, what are the velocities of the two objects after the collision? Give the velocity v_1 of object one, followed by object v_2 of object two, separated by a comma. Express each velocity in terms of v.

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Part B: v_1 = v_2 = \frac{v}{2}

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No loss of energy means that initial kinietc energy is the same as the final kinetic energy:

\frac{1}{2}(m_{1}.v_{1i} + m_{2}.v_{2i}) = \frac{1}{2} (m_{1}.v_{1f} + m_{2}.v_{2f}  )

To determine the final velocities of each object, there are 2 variables and two equations, so working those equations, the result is:

v_{2f} = \frac{2.m_{1} } {m_{1} + m_{2} }.v_{1i}  + \frac{(m_{2} - m_{1})}{m_{1} + m_{2} } . v_{2i}

v_{1f} = \frac{m_{2} - m_{1} }{m_{1} + m_{2} } . v_{1i} + \frac{2.m_{2} }{m_{1} + m_{2} } .v_{2i}

For all the collisions, object 2 is static, i.e. v_{2i} = 0

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v_1 = \frac{m_{2} - m_{1}}{m_{1} + m_{2} } . v_{1i}

v_1 = 0

v_2 = \frac{2.m_{1} }{m_{1} + m_{2}}.v_{1i}

v_2 = \frac{2.m}{m+m}.v

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When the masses are the same and there is an object at rest, the object in movement stops and the object at rest has the same same velocity as the object who hit it.

<u>Part B</u>: Same mass but collision is inelastic: An inelastic collision means that after it happens, the two objects has the same final velocity, then:

m_{1}.v_{1i} + m_{2}.v_{2i} = m_{1}.v_{1f} + m_{2}.v_{2f}

m_{1}.v_{1i} = (m_{1}+m_{2}).v_{f}

v_{f} =  \frac{m_{1}.v_{1i}}{m_{1} + m_{2} }

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v_1 = \frac{2m - m}{2m + m } . v

v_1 = \frac{v}{3}

v_2 = \frac{2.m_{1} }{m_{1} + m_{2}}.v_{1i}

v_2 = \frac{2.2m}{2m+m}.v

v_2 = \frac{4v}{3}

<u>Part D</u>: Object 1 is m, object is 3m and collision is inelastic:

v_1 = v_2 = v_{f} =  \frac{m_{1}.v_{1i}}{m_{1} + m_{2} }

v_1 = v_2 = \frac{m}{m+3m}.v

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