Hi, can you walk me through this question? The answer is apparently 1.798*10^5 N/m, but I keep on getting a wrong answer.
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Hi, can you walk me through this question? The answer is apparently 1.798*10^5 N/m, but I keep on getting a wrong answer.
Hi,
Thank you for your question.
Whenever you are solving these types of questions, use conservation of energy.
∑Ei + ∑Wfr = ∑Ef.
The final energy would be spring potential and the initial energy would be gravitational potential. Also, make sure to acknowledge that work is done by friction in two different places (on the ramp and on the horizontal)
I will lable work done by friction on the ramp as Wfr1 and work done by friction on the horizontal as Wfr2.
These would be the variables I would use:
L: length of the ramp
Θ1: angle of the ramp
Θ2: angle between friction force and displacement
d: compressed distance of the spring
sin30˚ = 20/L, L = 20/sin30˚
Ug + Wfr1 + Wfr2 = Us,
mgh + µmg(cosΘ1)L(cosΘ2) + µmgd(cosΘ2) = 1/2 (k)(d)^2
(85)(10)(20) + (0.3)(85)(10)(cos30˚)(20/sin30˚)(cos180˚) + (0.3)(85)(10)(0.3)(cos180˚) = 1/2 (k)(0.3)^2,
Now, solve for k.
8090.040881 = 0.045 k,
Hence, for the result, you would be getting k = 1.798*10^5 N/m.
Does this answer your question?