Scale Reading of Normal Force: Due by Midnight

AI Thread Summary
A scale measures the normal force, not actual weight, which is crucial for understanding the scenario of a student weighing himself on a skateboard rolling down an incline. The student, weighing 61 kg, experiences forces that must be analyzed using a free body diagram (FBD). The normal force and gravitational force need to be resolved into components parallel and perpendicular to the incline. Since there is no friction, the forces perpendicular to the incline must balance out, leading to a specific reading on the scale. The discussion emphasizes the importance of correctly interpreting the FBD and the forces involved to find the scale reading.
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Remember that a scale records the value of
the normal force, not a person’s actual weight.
Draw a FBD. Rotate your coordinate system.

A 61 kg student weighs himself by standing
on a scale mounted on a skateboard that is
rolling down an incline, as shown. Assume
there is no friction so that the force exerted
by the incline on the skateboard is normal to
the incline.
The acceleration of gravity is 9.81 m/s

What is the reading on the scale if the angle
of the slope is 29◦?
Answer in units of N

I have my free body diagram with Fn going up and to the left and Fg gong straight down. I do not understand how to rotate the FBD or what that would accomplish...
ANY HELP WOULD BE MUCH APPRECIATED!
 
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Your FBD is correct. Now break up the weight force into components parallel and perpendicular to the plane, and cross out the initial weight vector. The sum of forces perpendicular to the incline must equal zero, since the skateboarder does not lift off the incline in that direction.
 
much thanks! mission accomplished
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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