Alan G. answered • 05/23/16
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David,
What you need is the component of the acceleration due to gravity parallel to the ramp.
Since the object weighs 25 pounds and the acceleration due to gravity is 32 ft/s2, the component of the force parallel to the ramp is:
F = 25 sin (40°) = 16.07 lb.
Next, using Newton's Second Law, F = ma, you can find the acceleration for the object as it slides down the ramp by plugging in F = 16.07 lb and m = 25/32 slugs to solve for a.
Let me know if this helps you. I am not an expert in physics (by any means), but this is a fairly simple problem to solve. Feel free to send your answer back to me if you need it checked.
Alan G.
Its hard to say this without being able to draw a picture here, but I'll try.
The force parallel to the ramp points down the ramp. The force due to gravity points downward. The force with which the object pushes directly against the ramp is a third vector pointing downward and perpendicular to the ramp surface. Due to the moveability of vectors, these three forces can be rearranged to form a right triangle with the 40 degree angle at the bottom, the weight vector as the hypotenuse (I visualize this at the left of the triangle), and the force pulling the object down the ramp at the top. Using basic right triangle trig, the equation I set up to solve this should be apparent.
It's too bad we can upload or download pictures in WyzAnt, but the reason for this restriction is to protect the site and its users from viruses and information abuse.
Let me know if you require more explanation on this.
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05/24/16
David M.
05/24/16