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Sergeu [11.5K]
3 years ago
10

base your answer to this question on the information below and on your knowledge of physics. A toy launcher that is used to laun

ch 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. 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.
Physics
1 answer:
Nadya [2.5K]3 years ago
3 0

Answer: v = 2.24 m/s

Explanation: The <u>Law</u> <u>of</u> <u>Conservation</u> <u>of</u> <u>Energy</u> states that total energy is constant in any process and, it cannot be created nor destroyed, only transformed.

So, in the toy launcher, the energy of the compressed spring, called <u>Elastic</u> <u>Potential</u> <u>Energy (PE)</u>, transforms into the movement of the plastic sphere, called <u>Kinetic</u> <u>Energy (KE)</u>. Since total energy must be constant:

KE_{i}+PE_{i}=KE_{f}+PE_{f}

where the terms with subscript i are related to the initial of the process and the terms with subscript f relates to the final process.

The equation is calculated as:

\frac{1}{2}kx^{2}+0=0+\frac{1}{2}mv^{2}

\frac{1}{2}kx^{2}=\frac{1}{2}mv^{2}

\frac{1}{2}50(0.1)^{2}=\frac{1}{2}(0.1)v^{2}

v^{2}=\frac{50(0.1)^{2}}{0.1}

v=\sqrt{50(0.1)}

v=\sqrt{5}

v = 2.24

The maximum speed the plastic sphere will be launched is 2.24 m/s.

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