Conservation of energy / work problem

adams_695 · Aug 4, 2019

Handwritten worked solution on lined paper: Answer: vF^2 = vi^2 + 2gy - 2Fnc d/m, = (12 m/s)^2 + 2(9.8 m/s^2)(30 m) - 2(120 N)(450 m)/70 kg, vF = 24 m/s.

Handwritten work-energy derivation under the heading Attempt, solving for final speed v_F step by step from the energy equation with drag force, ending with v_F = square root of (v_i^2 - 2gy_f + 2gy_i - 2F_drag d / m).

Handwritten algebra attempt solving for v_f from the energy equation (1/2)mv_f^2 + mgy_f = (1/2)mv_i^2 + mgy_i - F_drag d, ending with v_f = sqrt(v_i^2 - 2g(y_f - y_i) - 2F_drag d / m).

If someone could advise what I've done wrong it would be much appreciated. How have they eliminated the initial and final for y, and simplify only to y? Also, how did they simplify to a positive 2? What algebraic steps have I missed? Thanks for your help.

haruspex · Aug 4, 2019

I would not call that a problem statement. What is the actual question?

adams_695 · Aug 4, 2019

haruspex said:

I would not call that a problem statement. What is the actual question?

Printed physics homework text showing the end of problem 7 about a plane landing on a spring, then problems 8 and 9: a frisbee stuck 16 m up in a tree, and a cyclist coasting down a 450-m slope.

Sorry here it is. Question 9. Thanks!

haruspex · Aug 4, 2019

You are told the top of the hill is 30m higher than the bottom of the hill. So what is y_i-y_f?

adams_695 · Aug 4, 2019

haruspex said:

You are told the top of the hill is 30m higher than the bottom of the hill. So what is y_i-y_f?

30m-0m.

Is this how I went wrong when solving algebraically in the image of my working?

Chandra Prayaga · Aug 4, 2019

There was nothing wrong in what you worked out. As haruspex pointed out, identify yi and yf in your own algebra and you are done.

haruspex · Aug 4, 2019

adams_695 said:

30m-0m.

Is this how I went wrong when solving algebraically in the image of my working?

The last line of your working has the terms -2gy_f+2gy_i. Factorise.

Conservation of energy / work problem

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