Mass on a ramp with friction discrepancy

AI Thread Summary
A 50kg mass on a 40° ramp experiences a frictional force with a coefficient of 0.1 while being pulled at a 15° angle above the ramp, accelerating at 1 m/s². The net force calculations indicate that the force required to maintain this acceleration is approximately 405.8N, which aligns with two other students' results. However, six other students and the teacher calculated the force to be around 350N, suggesting a potential sign error in their calculations. The discrepancy centers on the correct application of force components and the frictional force in the equations. The discussion highlights the importance of careful force analysis in physics problems.
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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?
 
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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.
 
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