Mass on a ramp with friction discrepancy

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SUMMARY

The problem involves a 50kg mass on a 40° ramp with a coefficient of kinetic friction of 0.1, being pulled at a 15° angle above the ramp and accelerating at 1 m/s². The calculated force required to maintain this acceleration is approximately 405.8N, as confirmed by multiple students. In contrast, a group of six students and the teacher arrived at a force of about 350N, likely due to a sign error in their calculations. The correct approach involves separating the net forces into x and y components and accurately applying the equations of motion.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Knowledge of frictional forces (Ff=μk*N)
  • Ability to resolve forces into components (x and y directions)
  • Familiarity with trigonometric functions in physics (sine and cosine)
NEXT STEPS
  • Review the application of Newton's Second Law in inclined planes
  • Study the effects of friction on motion in physics
  • Practice resolving forces into components using trigonometry
  • Explore common mistakes in force calculations, particularly sign errors
USEFUL FOR

Students studying physics, particularly those focusing on mechanics involving inclined planes and friction, as well as educators seeking to clarify common misconceptions in force calculations.

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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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