Motion in accelerated reference frame

[dowjonez]

i don't know why I am stuck on this question. It seems so easy, its making me sick.

question:
A man mounts a bathroom scale positioned on a skateboard such that it can roll without friction down an inclined plane of angle theta. He stands on the scale and reads off his weight as he is rolling down the inclined plane. What is the slope theta of the inclined plane if the scale displays 45kg during the descent and the actual mass of the man is 60kg?

The answer in the back says that theta = 30 degress


can anyone please give me some help with this question

 

[Mindscrape]

Uhhh, mass can't change. Are you sure this problem is right? Weight can vary, but mass cannot.

 

[dowjonez]

The question is right.

im sure the mass isn't changing, but the way the scales reads it is changing because its being accelerated

 

[dowjonez]

the bathroom scale measures the normal force upwards on the person. The normal force changes during acceleration. that's all i know

 

[franznietzsche]

Ok, this is just a basic balance of forces problem in a fancy wrapper.

Do a free body diagram for the man. The normal force is perpendicular to the incline, not the horizontal. The scale measures the vertical component of the normal force. You want a vertical component that is 45/60 = 3/4 of the gravitational force. Break the normal force into components, equate the y component to 45*9.8 N (hint: the y component should be a function of theta). Solve for theta.