How Do You Calculate the Acceleration and Direction of a Flea in a Breeze?

[jfeyen]

Homework Statement

A flea jumps by exerting a force of 1.20 X 10^-5 N straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of 0.500 X 10^-6 N on the flea. Find the direction and magnitude of the acceleration of the flea if its mass is 6.00 X 10^-7 kg. Do not neglect the force of gravity.

Homework Equations

a= net F / m
w=mg

The Attempt at a Solution

I went ahead and found the weight of the flea by multiplying its mass times gravity (6X10^-7)(9.8)= 5.88X10^-6 N which I'm assuming will be figured into the net F, but I'm not sure exactly where to go from here. Does weight need to be subtracted from the force of the flea on the ground and the force of the breeze on the flea? or does the weight and the force of the flea need to be subtracted from the force of the breeze? am I on the wrong track all together?? Do I need to somehow break it down into x and y components.. in which case I'm more lost than I thought. :)

Also, I suppose the weight needs to be figured into the direction? I tried tan^-1(.5X10^-6/1.2X10^-5) for an angle of 2.39^o but the answer in the back of the book is 4.68^o so obviously I don't know what I'm doing.

Thank you in advance for any help :)

 

[PhanthomJay]

The breeze force acts in the x direction, while the weight and ground forces act in the y direction. You have to look at the net forces in the x direction to solve for the acceleration in the x direction, then look at the net force in the y direction to solve for the acceleration in the y direction. Then the acceleration magnitude and direction comes from pythagorus' theorem and basic trig.

 

[jfeyen]

I guess I'm just having problems figuring out how to deconstruct this then. I think I was close to having everything snap into place in my mind, but it's gone. Is this the right idea? netF_y= F_flea-w= ma_y... a_y= 10.2m/s²? and netF_x= F_breeze= ma_x... a_x= .83m/s²?

 

[PhanthomJay]

I guess I'm just having problems figuring out how to deconstruct this then. I think I was close to having everything snap into place in my mind, but it's gone. Is this the right idea? netF_y= F_flea-w= ma_y... a_y= 10.2m/s²? and netF_x= F_breeze= ma_x... a_x= .83m/s²?

Yes, exactly (I didn't check your numbers, but your equations are correct).. Just be a bit more clear on the direction... Fnety is up...so ay is up..now solve for the mag and direction of a.

 

[rwisz]

I would approach this problem by first identifying the known values and variables. The known values are the force of the flea (1.20 X 10-5 N) and the force of the breeze (0.500 X 10-6 N) and the mass of the flea (6.00 X 10-7 kg). The variables are the acceleration of the flea (a) and the direction of the acceleration (θ).

Next, I would use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration (ΣF = ma). In this case, the net force is the sum of the force of the flea, the force of the breeze, and the force of gravity (weight).

So, the equation would be: (1.20 X 10-5 N + 0.500 X 10-6 N - 5.88 X 10-6 N) = (6.00 X 10-7 kg) a

Simplifying, we get: 6.12 X 10-6 N = (6.00 X 10-7 kg) a

Solving for acceleration, we get: a = 10.2 m/s^2

To find the direction of the acceleration, we can use trigonometry. The force of gravity acts straight down, so we can use the tangent function to find the angle θ.

tanθ = (0.500 X 10-6 N) / (1.20 X 10-5 N) = 0.0417

θ = tan^-1(0.0417) = 2.39°

However, this is the angle of the force of the breeze, not the angle of the acceleration. To find the angle of the acceleration, we need to add 180° to the angle of the force of the breeze, since the acceleration is in the opposite direction.

θ = 2.39° + 180° = 182.39°

So, the direction of the acceleration is 182.39° from the horizontal, in the direction opposite of the force of the breeze. The magnitude of the acceleration is 10.2 m/s^2.

In summary, to find the net force and direction of the acceleration, we need to take into account all the forces acting on the flea, including the force of gravity. We