Oh look, Twilight Sparkle and her boyfriend Spike in Physics exam, cool.

@Parcly Taxel  
When I went through college (yay for the US educational system…) we did problems like this in the intro to physics class, presumably in case students didn’t learn it in high school or had forgotten it by then. I took physics in high school, but the refresher was nice. Also at my high school, students had to take a science class but got to choose between physics, chemistry, and biology (and think one or two others, i don’t remember)

@Parcly Taxel  
I dunno: I’m not Peruvian.
 
My little bro learned this at about your age, too. Not me: Physics were not my thing, I “learned” all this a year later then you and then took a Humanistic Sciences educational path in order to avoid any kind of maths. I think I suffer from dyscalculia.
 
Kudos for being the one who solved this, and for the effort of explaining it so simply and plain.

@bigladiesman @FanOfMostEverything  
If this is a university question, I don’t know how good Peru’s educational system is. NUS High taught me how to tackle these problems in year 2 (13 to 14 years old, 8th grade). Let me tidy up the problem:

The last one is effectively asking for the minimum static coefficient, since any higher value will keep Spike in place too.
 
For now we can treat Spike and the box as a single 68 kg mass. If Twilight’s movement is east, the forces on the box/Spike combination are:  
-> Gravity (20° west of south)  
-> Normal (north)  
-> Twilight’s pull (east)  
-> Friction (west) at 0.2 of the normal force  
The gravity is a force of (58 + 10)g = 667.08 N and resolves to a south component of 626.85 N and a west component of 228.15 N. The normal force is therefore 626.85 N (the second question’s answer) too since only gravity opposes it - everything is in equilibrium here - and the friction is 0.2 of the normal or 125.37 N. Hence Twilight is supplying a force of 125.37 + 228.15 = 353.52 N (first question).
 
For the last question, the forces acting on Spike are:  
-> Gravity (20° west of south)  
-> Normal (north)  
-> Friction (east)  
The south component of the gravity - and normal force too - is 10g * cos 20 = 92.18 N and the west component is 10g * sin 20 = 33.55 N. The minimum static coefficient of friction possible is therefore 33.55 / 92.18 = 0.364.
 
That was easy, wasn’t it?

@LordDusk2014  
https://en.wikipedia.org/wiki/Pound_(force)  
https://en.wikipedia.org/wiki/Pound_(mass)  
There are two kinds of pounds. I’ve never heard of the poundal before. Interesting unit, but it doesn’t negate to fact that there is a unit of force that is called a pound.

@Drasvin  
Pounds measure mass; poundals measure weight.

@LordDusk2014  
One: I’m an American.  
Two: Mass is not the same thing as weight. Mass is the quantity of matter in a thing. Weight is the force applied to a mass by gravity and therefor can fluctuate based on location.  
Three: while the pound-mass is a thing (which I had forgotten it was) you need to specify that otherwise there’s going to be confusion and most people are going to assume you mean pound-force as that is the most common usage of the pound.  
Four: I think the conversation between kg to pound-mass and kg to pound-force assuming 1g are different. The wikipedia article for pound-mass lists 1 lbm as being 5/11 kg and also the ~2.2 conversion in US.
 
Yay for numbeted list to organize thoughts

@LordDusk2014  
It’s the “mass (weight)” comment that concerns me.

@FanOfMostEverything  
Pounds, not poundals…

@LordDusk2014  
Mass and weight are not interchangeable. Again, weight is force, mass times acceleration. There are different units at work.

@untraceablelarry  
@FanOfMostEverything  
@Drasvin  
I know; I was just converting the two masses to pounds. Oh, and FYI, pounds are used to measure mass (weight) in America.

@bigladiesman  

 
AUTO-FIXED. Sorry. I’d like to add the problem to the description if the OC has no inconvenient.

@FanOfMostEverything  
Yeah. The Imperial unit of mass is the slug.  
https://en.wikipedia.org/wiki/Slug_(mass)

@LordDusk2014  
Also, pounds are units of force, not mass. Your poundage changes depending on the strength of the local gravity.

@LordDusk2014  
You never use pounds in physics problems; always use SI units or units that easily convert to SI units

For those that use pounds:  
58kg = ~130lbs  
10kg = ~20lbs

@bigladiesman  

@Masem  
Sorry. You didn’t show your work. So you get a B instead.

@Masem  
Further evidence for her expression.
 
“‘Follow the script,’ they said. ‘Nopony will learn anything otherwise,’ they said. And they’re right, but that doesn’t mean I have to like it.”

@Masem  

 
Now it works.

Twilight would use magic to levitate the box and Spike, thus ignoring any forces involved.
 
I’ll take my A now.

They tell me it’s just basic physics. I dunno: in my country you can pass go to a superior level if you fail a maximum of two, so in middle school I skipped Physics/Chemistry and Math, and then chose a Humanistic Science curricular itinerary. College, and, ZALOOM, a Bachelor Degree in Library Science, like Twily here.

@FanOfMostEverything  
Oh right :-)

@bigladiesman  
My little bro (26) says he can solve this.