Starting from rest, a 2.4x10-4 kg flea springs straight upward. While the flea is pushing off from the ground, the ground exerts an average upward force of 0.42 N on it. This force does 1.5x10-4 J of work on the flea. (a) What is the flea's speed when it leaves the ground? (b) How far upward does the flea move while it is pushing off? Ignore both air resistance and the flea's weight.
at takeoff Ke = (1/2) m v^2 = 1.5*10^-4
solve that for v
work done = force * distance
1.5*10^-4 = .42 * distance
(a) Work = (1/2)MV^2 at takeoff
v = sqrt(2*2.4*10^-4/1.5*10^-4)
= 0.00017888543 j
still not right where am I going wrong?
1.5*10^-4 = (1/2) (2.4*10^-4) v^2
so
v^2 = 3/2.4 = 1.25
v = 1.11 m/s
I dont get how you got the unit m/s for v.. can you elaborate?
To solve this problem, we need to apply the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the flea by the ground is equal to the change in the flea's kinetic energy.
(a) To find the flea's speed when it leaves the ground, we need to find its final kinetic energy.
The work done on the flea is given as 1.5x10^-4 J. This work is done against the gravitational force, so it increases the flea's potential energy. Since there is no air resistance, we can assume that the flea's potential energy is converted entirely into kinetic energy.
If we denote the initial kinetic energy of the flea as Ki, and the final kinetic energy as Kf, then we have:
Work Done = Change in Kinetic Energy
1.5x10^-4 J = Kf - Ki
Since the flea starts from rest, its initial kinetic energy is zero, so we can simplify the equation to:
1.5x10^-4 J = Kf
To find the final kinetic energy, we use the formula for kinetic energy:
Kf = (1/2)mv^2
Where m is the mass of the flea and v is its final velocity. The mass of the flea is given as 2.4x10^-4 kg. Substituting these values into the formula, we get:
1.5x10^-4 J = (1/2)(2.4x10^-4 kg)v^2
Simplifying the equation, we find:
v^2 = (1.5x10^-4 J) / (1.2x10^-4 kg)
v^2 = 1.25 m^2/s^2
Taking the square root of both sides, we find:
v = 1.12 m/s
So, the flea's final speed when it leaves the ground is 1.12 m/s.
(b) To find how far upward the flea moves while it is pushing off, we can use the work-energy principle again.
The work done on the flea by the ground is equal to the change in its potential energy:
Work Done = Change in Potential Energy
1.5x10^-4 J = mgh
Where m is the mass of the flea, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height the flea moves upward.
Since the potential energy is given by P.E = mgh, we can rearrange the equation to solve for h:
h = (1.5x10^-4 J) / (mg)
Substituting the values of m and g, we get:
h = (1.5x10^-4 J) / (2.4x10^-4 kg × 9.8 m/s^2)
h ≈ 6.80 m
Therefore, the flea moves approximately 6.80 meters upward while it is pushing off.
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