Mass on a ramp with friction discrepancy

Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
1 reply · 2K views
Questlove
Messages
2
Reaction score
0

Homework Statement


A mass of 50kg is on a ramp 40° above the ground. The coefficient of kinetic friction for the surface of the ramp is .1. If the mass is pulled by a force 15° above the ramp and accelerates at 1 m/s^2 up the ramp, what is the magnitude of the force?

Homework Equations


Ff=μk*N
F=ma

The Attempt at a Solution


First I separated each net force into x (horizontal to ramp) and y (perpendicular to ramp) components. Also, the net force in the x direction must be 50N up the ramp, since 50kg*1 m/s^2=50N. Also, the net force in the y direction must be 0 since the mass is staying on the ramp.
Fnet x: 50 = F*cos(15°)-(Ff+sin(40°)*50*9.8) = F*cos(15°)-(Ff+314.97)
Fnet y: N + F*sin(15°) = cos(40°)*50*9.8 = 375.36

Since μk=.1 is given, Ff=.1*N

I replaced Ff with .1*N in the x equation, getting:
50=F*cos(15°)-.1*N-314.97

Then I replaced N with 375.36-F*sin(15°), getting:
50=F*cos(15°)-.1*(375.36-F*sin(15°))-314.97

From here, I solved for F to get an answer of about 405.8N, which was matched by 2 other students who both did the same problem individually. The discrepancy is that 6 other students, as well as my teacher, got answers of about 350N. Who is right, and why is the wrong group wrong?
 
Physics news on Phys.org
Your math seems to check out. i feel as though the group of six and the teacher may be wrong due to a sign error.