Answer:
A) The elastic potential energy stored in the spring when it is compressed 0.10 m is 0.25 J.
B) The maximum speed of the plastic sphere will be 2.2 m/s
Explanation:
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<em>A toy launcher that is used to launch small plastic spheres horizontally contains a spring with a spring constant of 50. newtons per meter. The spring is compressed a distance of 0.10 meter when the launcher is ready to launch a plastic sphere.</em>
<em>A) Determine the elastic potential energy stored in the spring when the launcher is ready to launch a plastic sphere.</em>
<em>B) The spring is released and a 0.10-kilogram plastic sphere is fired from the launcher. Calculate the maximum speed with which the plastic sphere will be launched. [Neglect friction.] [Show all work, including the equation and substitution with units.]</em>
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A) The elastic potential energy (EPE) is calculated as follows:
EPE = 1/2 · k · x²
Where:
k = spring constant.
x = compressing distance
EPE = 1/2 · 50 N/m · (0.10 m)²
EPE = 0.25 J
The elastic potential energy stored in the spring when it is compressed 0.10 m is 0.25 J.
B) Since there is no friction, all the stored potential energy will be converted into kinetic energy when the spring is released. The equation of kinetic energy (KE) is the following:
KE = 1/2 · m · v²
Where:
m = mass of the sphere.
v = velocity
The kinetic energy of the sphere will be equal to the initial elastic potential energy:
KE = EPE = 1/2 · m · v²
0.25 J = 1/2 · 0.10 kg · v²
2 · 0.25 J / 0.10 kg = v²
v = 2.2 m/s
The maximum speed of the plastic sphere will be 2.2 m/s
