A Problem Involving Newton's Second Law

AI Thread Summary
A sky-diver experiences two forces: the downward gravitational force (Fg = mg) and the upward drag force (Fr), which is proportional to velocity (Fr = bv). Applying Newton's Second Law, the net force can be expressed as the difference between these forces, leading to the equation ma = mg - bv. This can be rearranged to express acceleration (a) as a function of velocity (v), resulting in a = g - (b/m)v. The discussion highlights the importance of correctly defining the drag force in relation to velocity to solve the problem effectively.
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Once her chute opens, a sky-diver of mass m is acted upon by a downward force Fg due to gravity, and an upward force Fr due to air resistance. If Fg = mg, where g is gravitational acceleration, and Fr is proportional to velocity v, use Newton’s Second Law of Motion to write acceleration a as a function of velocity v.

Hey guys, I need a help on how to approach this problem. Initially, I assumed Fr = Ff = umg. But the problem states that Fr is proportional to velocity. Help?
 
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Newton's 2nd law is
\sum_i \mathbf{F}_i = m\mathbf{a}What do you get when you apply it to this problem?
 
Proportional meaning, the upward force equals the velocity, times a proportionally constant. Hence the drag force is Fr=bv, where b is a real number and v is velocity.
 
Xyius said:
Proportional meaning, the upward force equals the velocity, times a proportionally constant. Hence the drag force is Fr=bv, where b is a real number and v is velocity.

Thanks Xyius! Using your definition of drag force, I was able to work it out!
 
Glad to hear it! :D!
 
Would you care to explain how you did this?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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