Eksperimentti: hyppykorkeuden määrittäminen impulssilla: Difference between revisions
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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

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