Mass on a ramp with friction discrepancy

In summary, a mass of 50kg on a ramp with a coefficient of kinetic friction of .1, pulled by a force 15° above the ramp and accelerating at 1 m/s^2, has a net force of 50N in the x direction and 0 in the y direction. Using this information and the equations F=ma and Ff=μk*N, the magnitude of the force is calculated to be approximately 405.8N. This is confirmed by two other students, but six other students and the teacher arrived at a different answer of approximately 350N, which may be due to a sign error.
  • #1
Questlove
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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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  • #2
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.
 

FAQ: Mass on a ramp with friction discrepancy

What is "Mass on a ramp with friction discrepancy"?

Mass on a ramp with friction discrepancy refers to a scenario in which an object is placed on a ramp and experiences a difference in the expected amount of friction, which can affect its motion and acceleration.

Why does a mass on a ramp with friction discrepancy occur?

A mass on a ramp with friction discrepancy can occur due to various factors, such as the roughness of the ramp surface, the weight and shape of the object, and the presence of external forces.

How does the difference in friction affect the motion of the object?

The difference in friction can affect the motion of the object by either increasing or decreasing its acceleration, depending on the direction and strength of the friction force. This can result in a discrepancy between the expected and actual motion of the object.

What are some ways to reduce the discrepancy in friction on a ramp?

Some ways to reduce the discrepancy in friction on a ramp include using a smoother surface, adjusting the angle of the ramp, and minimizing the weight and surface area of the object.

What are some real-world applications of studying "Mass on a ramp with friction discrepancy"?

Studying "Mass on a ramp with friction discrepancy" can have various real-world applications, such as understanding the motion of objects on inclined planes, designing more efficient ramps and roller coasters, and improving the performance of vehicles on different surfaces.

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