Question

Starting from rest, a 1.7 10-4-kg flea springs straight upward. While the flea is pushing off from the ground, the ground exerts an average upward force of 0.37 N on it. This force does +2.1 10-4 J of work on the flea.

(a) What is the flea's speed when it leaves the ground?

_______ m/s
(b) How far upward does the flea move while it is pushing off? Ignore both air resistance and the flea's weight.
  _______ m

Answer 1

By the Work- energy theorem is

" The work done by the force is numerically equal to change in
Kinetic energy "

Given:
Mass of the flea = M = 1.7*10^-4 kg
While the flea is pushing off from the ground,   
  
the ground exerts an average upward force of F = 0.37 N

work on the flea by this force W = 2.1*10^-4 J

since , flea is starting from rest, its intial K.E = 0  

Let , V be the speed of the flea when it leaves the ground

Thus, K.E of the flea at this point = 1/2 *M*V^2

The change in K.E = final K.E - intial K.E = 1/2 *M*V ^2  

work done W = average upward force x displacement ( How far upward does the flea move )
  
work done W = force (F) * flea move distance( d) = change in K.E = 1/2 *M*V^2 ---------------------(1)

(a)
from equation 1  

W = 1/2 *M*V^2

(2.1*10^-4) = 1/2 *(1.7*10^-4)(V)^2

V = 1.571 m/s  

speed of the flea when it leaves the ground is V = 1.571 m/s

(b)

W = F . d  

flea move distance d = W / F

= (2.1*10^-4) / ( 0.37 )
  
= 5.675*10^-4 m
  
flea move while it is pushing off = 5.675*10^-4 m