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I am doing an experiment to show the effect on the velocity of a falling mass due to change in mass. How can i justify my prediction that the velocity of the falling mass will increase as i increase the mass.

For my experiment i am dropping masses between 100-800g threw 1000ml of water and timing how long the mass takes to fall the 35cm height. From my results i can see that as the mass increases the time taken for the mass to reach the bottom of the 35cm decreases. Is this due to change in velocity and am i correct in using velocity and mass as my measurements?

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  • $\begingroup$ You need to quantify drag force, or is this done in a vacuum? Have you seen the famous Apollo astronaut hammer and feather drop video? $\endgroup$ – ja72 Oct 9 '13 at 3:26
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While I don't want to give away the "correct answer" I would like to direct you a little.

  • What forces are acting on the objects to make it fall?
  • What other forces are acting on the objects that might change how fast it falls? (hint: think of friction)
  • How would these forces compare in other environments like air or in a vacuum?
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How about stoke's law: http://en.wikipedia.org/wiki/Stokes%27_law

If your masses are spherical and of same radius, you can easily compute the $v_s$ terminal (or settling) velocity (i.e. the velocity at which the sphere will fall in the fluid). Se the equation for $v_s$ in the "Terminal Velocity of Sphere Falling in a Fluid" section. There $v_s$ is shown to be linear in the sphere mass (since it depends linearly on the mass density $\rho_p$ and the $m_p$ mass is $m_p = \rho_p { 4 \over 3} \pi R^3$).

Thus if your experiments involve spheres of different densities, you should detect that the velocity has an approximate linear dependency on the sphere mass. It's only approximate since the terminal velocity is attained after a transient motion (the actual sphere velocity $v(t)$ is modeled by $v(t)=v_s \tanh(\beta t)$, where $\beta > 0$ depends on fluid viscosity&density and sphere density&radius, see http://en.wikipedia.org/wiki/Terminal_velocity). After the transient (say for $t > t_T = 3 \times {1 \over \beta}$, i.e. $\tanh(3) \sim 0.995$), the sphere is falling at constant velocity (drag, buoyancy and gravity forces are balanced). Thus if the distance to fall in the fluid (and thus the time falling in the fluid) is increased (say to allow to be well after the transient), then the mass-dependency would be remarkably more linear (since the tanh gets closer to 1 as time of fall increases).

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