Eksperimentti: hyppykorkeuden määrittäminen impulssilla: Difference between revisions

From wikiluntti
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\end{align}
\end{align}
</math>
</math>
The takeoff velocity is <math>v_0 = \frac Jm = \frac{445.25 Ns}{89.7 kg} = 4.96 m/s</math>.


== Example 2: Zero the force plate ==
== Example 2: Zero the force plate ==

Revision as of 19:14, 3 May 2022

Introduction

Force exerted on the force plate

Jumping on the force plate you can feel the force. We use time of flight method to estimate the height of the jump.

Theory

Impulse . Actually is our takeoff speed because , and we have . Because and thus we have because and . However, for the velocity we have Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v = v_0 - gt} and at the maximum height we have that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v=0} , and thus Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_0 = gt} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t=\frac{v_0}{g}} . Combining these two we have

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} h &= v_0 t - \tfrac12 gt^2 \\ &= v_0 \tfrac{v_0}g - \tfrac12 g\left( \frac{v_0}g \right)^2 \\ &= \frac{v_0^2}{g} - \tfrac12 \frac{v_0^2}{g} \\ &= \frac{v_0^2}{2g} \\ &= \frac{J^2}{2gm^2} = \frac{1}{2g} \left( \frac Jm \right)^2 \end{align} }

Note that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J/m = v_0} , and thus the equation gives the correct equation.

Example

The example gives

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} m &= 880 N /9.81 = 89.7 kg \\ J &= 700 Ns - 89.7 kg \times 9.81 \times 0.2895 s = 700 Ns - 254.75 Ns = 445.25 Ns \end{align} }

and thus we have

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} h &= \frac{J^2}{2gm^2} \\ &= \frac{(445.25 Ns)^2}{2 \times 9.81 m/s^2 \times (89.7 kg)^2 } \\ &= \frac{198 247. 5625}{315 728.5716} \\ &= 0.63 m\\ \end{align} }

The takeoff velocity is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_0 = \frac Jm = \frac{445.25 Ns}{89.7 kg} = 4.96 m/s} .

Example 2: Zero the force plate

References

https://www.thehoopsgeek.com/the-physics-of-the-vertical-jump/

https://www.brunel.ac.uk/~spstnpl/LearningResources/VerticalJumpLab.pdf