- #1
Eclair_de_XII
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- 91
Homework Statement
"A block is projected up a frictionless inclined plane with initial speed v0 = 3.5 m/s. The angle of incline is Φ = 32°. (a) How far up the plane does the block go? (b) How long does it take to get there? (c) What is its speed when it gets back to the bottom?"
Homework Equations
##v=v_0+at##
Answer as given by book: (a) 1.18 m; (b) 0.674 s; (c) 3.5 m/s
The Attempt at a Solution
##\vec v_0=(2.97i+1.85j)\frac{m}{s}##
Now, I figure there's downward acceleration from the normal force and gravity. I set the mass of the block (which originally was not specified) to 1 kg, to simplify my calculations.
##F_N=(sin238°)(1kg)(9.8\frac{m}{s^2})=-8.31N##
##F_g=(cos238°)(1kg)(9.8\frac{m}{s^2})=-5.19N##
So, given this, I find the acceleration for a mass that I invented for the block.
##\vec a = (-8.31i-5.19j)\frac{m}{s^2}##
Then I reduce the initial velocity to zero to find the time, which does not correspond with the answer given by the book.
##-1.85\frac{m}{s}=-9.8\frac{m}{s^2}t##
##t=0.189 s##
As you can see, this number does not match up with the answer as given by the book. Also, I just realized that it should be 32 degrees, and not 36 degrees in the FBD I drew on Paint.