Starting from rest, a 1.6x10-4 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 3.6x10-4 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.

(a) Work = (1/2)MV^2 at takeoff.

Solve for V
V = sqrt(2*3.6*10^-4/1.6*10^-4)

(b) Work = (avg. force)*(pushoff distance)
Solve for the pushoff distance

To solve this problem, we can use the work-energy principle, which states that the work done on an object equals the change in its kinetic energy.

(a) The work done on the flea is equal to the change in its kinetic energy. In this case, the work done is given as 3.6x10^-4 J. Since the flea starts from rest, its initial kinetic energy is zero. Therefore, we can write:

Work done = change in kinetic energy

3.6x10^-4 J = 1/2 * mass * final velocity^2

Plugging in the values:
3.6x10^-4 J = 1/2 * 1.6x10^-4 kg * final velocity^2

Now, solve for the final velocity:

final velocity^2 = (2 * 3.6x10^-4 J) / (1.6x10^-4 kg)
final velocity^2 = 7.2 m^2/s^2
final velocity = √(7.2 m^2/s^2)

Therefore, the flea's speed when it leaves the ground is approximately 2.68 m/s.

(b) To find the distance upward the flea moves while pushing off, we can use the work done by the ground. The work done by a force is equal to the force times the displacement in the direction of the force.

Work done = force * displacement

In this case, we know the force exerted by the ground to be 0.42 N. Let's assume the flea moves upwards by a distance of d. The work done can be calculated as:

0.42 N * d = 3.6x10^-4 J

Solving for d:

d = (3.6x10^-4 J) / (0.42 N)
d = 8.57x10^-4 m

Therefore, the flea moves approximately 8.57x10^-4 m upward while it is pushing off.

To solve this problem, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

(a) First, let's find the change in kinetic energy of the flea. Since the flea starts from rest, its initial kinetic energy is zero.

We are given that the work done on the flea is 3.6x10^(-4) J. This work is done by the ground in pushing the flea upward. So, the work done is equal to the change in kinetic energy:

Work = ΔK.E.

3.6x10^(-4) J = ΔK.E.

The final kinetic energy (K.E.) of an object can be calculated using the equation:

K.E. = 0.5 * mass * velocity^2

Since the flea is moving straight upward, we can use the final velocity as the flea's speed when it leaves the ground.

Substituting the given values,

3.6x10^(-4) J = 0.5 * (1.6x10^(-4) kg) * (velocity)^2

Solving for the velocity, we find:

velocity^2 = (2 * 3.6x10^(-4) J) / (1.6x10^(-4) kg)
velocity^2 = 7.2 m²/s²
velocity = sqrt(7.2) m/s

Therefore, the flea's speed when it leaves the ground is approximately 2.68 m/s.

(b) To find the distance the flea moves upward while pushing off, we need to calculate the work done on the flea by the upward force exerted by the ground.

We are given that the average upward force exerted by the ground is 0.42 N. The work done by this force can be calculated using the equation:

Work = force * distance

Since the flea is moving straight upward, the work done is equal to the change in potential energy (P.E.) of the flea.

Substituting the given values,

0.42 N * distance = 3.6x10^(-4) J

Solving for distance, we find:

distance = (3.6x10^(-4) J) / (0.42 N)
distance = 8.57x10^(-4) m

Therefore, the flea moves approximately 8.57x10^(-4) meters upward while pushing off.