Researchers often use force plates to measure the forces that people exert again

Question

Researchers often use force plates to measure the forces that people exert against the floor during movement. A force plate works like a bathroom scale, but it keeps a record of how the reading changes with time. (Figure 1) shows the data from a force plate as a woman jumps straight up and then lands. Suppose that ?t = 0.28s . Part A What was the vertical component of her acceleration during push-off? The positive direction is upward. Part D What was her speed as her feet left the force plate? Express your answer to two significant figures and include the appropriate units. Part E How high did she jump? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A)

At push-off,

Force on from the surface , F = 1000 N

Force due to gravity = mg

So, net force, Fnet = 1000-mg = m*a

verical component of acceleration(during push-off), a = F/m = 1000/m

Now m can be calculated by the force she exerts when still(= 500 N),

So, m = F(still)/g = 500/9.8 = 51.02 kg

So, F - mg = ma

So, a = (F-mg)/m = F/m - g = 1000/51.02 - 9.8 = 9.8 m/s2<-------answer

D)

We know, F*t = change in momentum

So, During pushoff,change in momentum, m(v-0) = (1000-mg)*0.28 = (1000-51.02*9.8)*0.28 = 140 kgm/s

So, v = 140/m = 140/51.02 = 2.75 m/s <--------answer

E)

Using conservation of energy,

Initial Kinetic energy when at the ground, K.E = 0.5*mv^2

Final Potential Energy when at top of her flight = mgh <--- here h = height reached

So, by work energy principle, K.E will be converted to P.E

So, 0.5*mv^2 = mgh

So, h = v^2/2g = 2.74^2/(2*9.8) = 0.38 m <---------answer

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