Question

Describe the motion of a body moving along a frictionless inclined plane.?
How is it compared with the motion of a freely falling body?

Answer 1

@Shane_B

Answer 2

don't keep me waiting :)

Answer 3

Gimme two more minutes....I typed it all out twice but didn't think I was explaining well.

Answer 4

wow..thanks a lot!! :) take your time then lol

Answer 5

Assuming the free falling object is going straight down...the only motion will be in the vertical direction and its velocity will only be influenced by the acceleration due to gravity (acting straight down) and drag/wind. The velocity at any point in time will be:\[V_{at \space t}=V_{initial}+acceleration* time\]

On a frictionless inclined plane however, the motion will be in two directions and the force due to gravity (unless the angle is exactly 45 degrees) will be different in each direction. Since the mass of the object is presumably constant that means the acceleration in both directions will be different. The image I posted shows you how to calculate the forces in each direction and from there you can calculate the acceleration and velocity for each component of the vector.

Answer 6

I find that the body accelerates downward at \[ g \sin^2 \theta\] and horizontally at \[\frac{1}{2} g \sin 2 \theta\] where theta is the angle of inclination.

Answer 7

Of course, if it were freely falling, it would simply accelerate downward at g.

Answer 8

@Shane_B can you just summarize? :) pls.?

Answer 9

I guess so :)

1) The free-falling object will accelerate at a rate of g (ie 9.8m/s^2) straight down ignoring drag. The velocity vector will only be in one direction (down).

2) The object on an inclined plane will accelerate at a rate proportional to g based on the angle of the incline. The acceleration and velocity vectors with have both x and y components.

Answer 10

*"with" = "will" in that last sentence