Penguin sliding up a ramp with friction

[isukatphysics69]

1. Homework Statement
in picture

Homework Equations

The Attempt at a Solution

in picture, not sure if i am even doing this properly but i think i am? i am going to continue trying part b but please if you can let me know if i am doing this proper let me know...Thank you

 

[kuruman]

Your work so far is probably OK but it is hard to follow what you are doing because you are substituting numbers right from the start. It is best to find an expression in terms of symbols giving the minimum force in part (a) in terms of symbols not numbers. Use W = weight of penguin, θ = incline angle, μ_s = coeff. static friction, μ_k = coeff. of kinetic friction, F_min = minimum force, F_max=maximum force, F_const = force needed to have the system move at constant velocity. Believe me, if you do this it will pay off in the end because essentially the same equation in terms of symbols answers all the parts with some minor adjustments. Furthermore, you will be able to see the bigger picture of what's going on.

 

[isukatphysics69]

Your work so far is probably OK but it is hard to follow what you are doing because you are substituting numbers right from the start. It is best to find an expression in terms of symbols giving the minimum force in part (a) in terms of symbols not numbers. Use W = weight of penguin, θ = incline angle, μ_s = coeff. static friction, μ_k = coeff. of kinetic friction, F_min = minimum force, F_max=maximum force, F_const = force needed to have the system move at constant velocity. Believe me, if you do this it will pay off in the end because essentially the same equation in terms of symbols answers all the parts with some minor adjustments. Furthermore, you will be able to see the bigger picture of what's going on.

okay thank you for the tip, my professor does this too i should probably adapt that habit.

 

[kuruman]

okay thank you for the tip, my professor does this too i should probably adapt that habit.

I agree with your professor 200%. It's a good habit because
(a) You can enter the formula and the input variables in something like a spreadsheet and calculate the answer in no time. This eliminates or helps troubleshoot calculation errors because recalculation is easy.
(b) If the answer is incorrect you can troubleshoot it by performing dimensional analysis and, if that fails, check your algebra easily lest you forgot a given quantity, squaring what needs to be squared, starting with an incorrect equation, etc.

 

[isukatphysics69]

ok for part b i am getting 46.2 Newtons

Answers = a.)8.6N, b.) 46.2N, c.) 38.6N

 

[haruspex]

ok for part b i am getting 46.2 Newtons

Answers = a.)8.6N, b.) 46.2N, c.) 38.6N

Those all look right.

 

[kuruman]

Those all look right.

I agree.

 

[isukatphysics69]

YES! Thank you guys