A dated box of dates, of mass 5.00 kg, is sent sliding up a frictionless ramp at an angle of θ to the horizontal. The figure below gives, as a function of time t, the component vx of the box's velocity along an x axis that extends directly up the ramp. (The vertical axis is marked in increments of 1.5 m/s.) What is the magnitude of the normal force on the box from the ramp?
Note: Does the notation of v having the subscript x have anything to do with my error? I'm assuming that the x is redundant, since the velocity's directed up the ramp entirely...right?
I'm assuming Newton's second law is in effect here?
The Attempt at a Solution
My roommate and I both tried this question. We got an answer around 48 each and every time, and the question answer is not given (it's a input-answer-and-we-tell-you-if-it's-wrong-or-right website).
I drew a ramp and stuff, writing the force vectors all over the place and determined that at the box's highest point on the ramp, the net forces would equal zero (my roommate said that this is wrong, but I still got the same answer as he did).
From the graph given, I found the deceleration of the box to be ~1.875 m/s2. From here, I have no idea where to go. I thought you needed to find theta, but my roommate said you could also use Pythag's theorem. We've gotten ~48 about four times now.
We worked out a triangle, with hypotenuse Fw = mg, and the x-component of Fw = mgsinθ, the y-component of Fw = mgcosθ.
Solving with Pythag's, we have
sqroot(9.82 - 1.8752) = normal acceleration
We then multiplied that normal acceleration by the mass and obtained out ~48 answer.
Our answers so far (that we submitted and the machine told us we were wrong): 47.96873982, 48.09479572
Any help is appreciated! Sorry if I did something wrong, this is my first post...:shy: