Finding acceleration of flea using force analysis

[mkwiatko]

Homework Statement

A flea jumps by exerting a force of 1.20x10-5 N straight down on the ground. A
breeze blowing on the flea parallel to the ground exerts a force of 0.500x10-6 N on the
flea. Find the direction and magnitude of the acceleration of the flea if its mass is
6.00x10-7 kg. Do not neglect the force of gravity.

Homework Equations

F = ma

F= sum of Fx + sum of Fy

weight = mg

The Attempt at a Solution

I figured the normal force exerted on the flea is flea's weight plus the force it exerts on the ground when it jumps. So, I used weight = mg to find the flea's weight and added it to 0.500x10-6N which equaled 1.79x10-5N. I then thought the only horizontal force was the force of the wind so that's what the sum of Fx equals. The sum of Fy equals the normal force minus the weight of the flea (which is 5.88X10-6N). I then added Fx and Fy, which equals 1.25x10-5N, to get F and set it equal to ma. I then divided 1.25x10-5N by the mass of the flea to get the acceleration. Is this right? The magnitude of acceleration I got seems high (20.8 m/s^2). Also, how do I determine the direction of acceleration?

 

[PeterO]

Homework Statement

A flea jumps by exerting a force of 1.20x10-5 N straight down on the ground. A
breeze blowing on the flea parallel to the ground exerts a force of 0.500x10-6 N on the
flea. Find the direction and magnitude of the acceleration of the flea if its mass is
6.00x10-7 kg. Do not neglect the force of gravity.

Homework Equations

F = ma

F= sum of Fx + sum of Fy

weight = mg

The Attempt at a Solution

I figured the normal force exerted on the flea is flea's weight plus the force it exerts on the ground when it jumps. So, I used weight = mg to find the flea's weight and added it to 0.500x10-6N which equaled 1.79x10-5N. I then thought the only horizontal force was the force of the wind so that's what the sum of Fx equals. The sum of Fy equals the normal force minus the weight of the flea (which is 5.88X10-6N). I then added Fx and Fy, which equals 1.25x10-5N, to get F and set it equal to ma. I then divided 1.25x10-5N by the mass of the flea to get the acceleration. Is this right? The magnitude of acceleration I got seems high (20.8 m/s^2). Also, how do I determine the direction of acceleration?

You are trying to find the acceleration of the flea, so should not include the force the flea exerts on the ground, but the force the ground exerts on the flea [Newtons 3rd Law: action Reaction pair]. That force is up, the weight force is down, so they do not just arithmetically add together.

For the Direction you use Trig.

 

[gneill]

Perpendicular vector components don't add as a simple sum. They add in quadrature. That is, you take the square root of the sum of the squares of the components. So where you say you added Fx and Fy, that is an incorrect operation.

Instead, calculate the vertical and horizontal accelerations separately from their respective net forces. Sum the acceleration component as the square root of the sum of squares to find the magnitude of the net acceleration. The direction of the acceleration is computed from the components, too: Use the arctan() function appropriately.

 

[PeterO]

Homework Statement

A flea jumps by exerting a force of 1.20x10-5 N straight down on the ground. A
breeze blowing on the flea parallel to the ground exerts a force of 0.500x10-6 N on the
flea. Find the direction and magnitude of the acceleration of the flea if its mass is
6.00x10-7 kg. Do not neglect the force of gravity.

Homework Equations

F = ma

F= sum of Fx + sum of Fy

weight = mg

The Attempt at a Solution

I figured the normal force exerted on the flea is flea's weight plus the force it exerts on the ground when it jumps. So, I used weight = mg to find the flea's weight and added it to 0.500x10-6N which equaled 1.79x10-5N. I then thought the only horizontal force was the force of the wind so that's what the sum of Fx equals. The sum of Fy equals the normal force minus the weight of the flea (which is 5.88X10-6N). I then added Fx and Fy, which equals 1.25x10-5N, to get F and set it equal to ma. I then divided 1.25x10-5N by the mass of the flea to get the acceleration. Is this right? The magnitude of acceleration I got seems high (20.8 m/s^2). Also, how do I determine the direction of acceleration?

BTW, I have seen many a "nature" program that claims that a flee has the greatest acceleration of and animal/insect on the planet, so are you sure that 20.8 ms^-2 is out of the question?
Did you use Pythagorus during your calculations, because you should have.

 

[rwisz]

Your approach to solving this problem is correct. However, there are a few things that can be improved upon. Firstly, the normal force exerted on the flea should not include the force it exerts on the ground when it jumps. The normal force is simply the force that balances the weight of the flea, so it should only be equal to the weight of the flea (5.88x10-6N). Secondly, when finding the sum of Fy, it should be the weight of the flea minus the normal force (5.88x10-6N - 1.79x10-5N = -1.20x10-5N). This negative sign indicates that the force is acting in the opposite direction of the positive y-axis (downward). Lastly, to determine the direction of acceleration, you can use the sign of the answer you get for the acceleration. In this case, since the acceleration is positive (20.8 m/s^2), it means that the flea is accelerating in the positive x-direction (towards the wind). If the acceleration had been negative, it would mean that the flea is accelerating in the negative x-direction (opposite the wind). Keep in mind that acceleration is a vector quantity, meaning it has both magnitude and direction. So, the magnitude of the acceleration you calculated is correct, but the direction should be towards the wind. Great job on using the correct equations and solving the problem!