A 86kg person jumps and plunges 2.6m deep into water before coming to a stop. How can I find the force of friction from the water?

Question

Their velocity before hitting the water is $10.48m/s$, and I want to use the conservation of energy formulas. I also went ahead and calculated the acceleration $(13.62m/s^2)$(edit: its $21.12m/s^2$), in hopes that would help, by using $F=ma$, but that's not how you calculate friction, haha...

I'm a high school student in Physics 11, and amidst this pandemic, it is very difficult to understand our new unit, so it's very frustrating that I'm not doing so well on the practice. Any and all help is appreciated! I just wish to better understand this unit before school is over.

How did you get $13.62 \text{m}/\text{s}^2$ for the acceleration? — Brian Tung, May 19 '20 at 23:07
I used the formula vf2 = vi2 +2ad and configured it to find a=vf^2-vi^2/2d ... vf^2 being 0, vi^2 = (10.48)^2, and d=-2.6 (negative because its below water's surface) — Lean Summers, May 19 '20 at 23:45
ooh! right! thanks hhaha I'll change the question up, miscalculation my part hehe must of forgot to square it in the calculator — Lean Summers, May 19 '20 at 23:47

score 1 · Answer 1 · answered May 20 '20 at 00:41

A body immersed in the water remains floating (more or less up to the kin) because of buoyancy: the famous eureka of Archimedes ! Buoyancy (almost) compensates for gravity.

So, when immersed, you can assume that the potential energy of gravitation+ buoyancy is almost null.

So the kinetic energy at entering the water will be mainly dissipated by friction. The friction force depends very much on the speed, however its average value will be such as to do a work equal to $F_f \cdot 2.6$ Joule, which shall null the kinetic energy of $1/2*86*(10.48)^2$, i.e. $F_f = 1816 N$ or about 182 kg.

score 0 · Answer 2 · answered May 19 '20 at 23:54

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There are two equivalent ways. One, calculate the acceleration using $v_f=0$:$$v_f^2=v_i^2+2ad$$so $$a=\frac{v_i^2}{2d}$$ Then the force acting on the body is $F=ma$. But note that $F$ is the sum of the forces. Gravity is acting downwards and friction is up. So $$F_f-mg=ma=m\frac{v_i^2}{2d}$$ The equivalent way to get the formula you get from energy. If you would multiply the above by $d$ and rearranging terms, you get $$F_f d=\frac{mv_i^2}2+mgd$$ The meaning of this is to say that the initial energy (kinetic+potential) is equivalent to the work done by friction

answered May 19 '20 at 23:54

Andrei

37,370

when inside the water, gravity is compensated by buoyancy, which is not to be accounted as "friction". – G Cab May 20 '20 at 00:21
True. If the volume of the person is finite. If not, then there is only friction. – Andrei May 20 '20 at 00:44

A 86kg person jumps and plunges 2.6m deep into water before coming to a stop. How can I find the force of friction from the water?

2 Answers2