You observe a block sliding down an incline and your careful measurements reveal

ID: 2127229 • Letter: Y

Question

that the angle, ?, of the incline is 18.0o, and that the block is sliding down the incline

at a constant speed. In order to explore this interesting physical problem, you

project the block back up the ramp with an initial speed of 2.00 m/s.

a.) Find an algebraic expression (one without any numerical values) for d, the

distance that the block will slide up the incline before coming to rest.

b.) Find a numerical value for d.

c.) After the block comes to rest, will it slide down the incline again? Give an

argument to back your answer.

NOW AS IT IS SLIDING DOWN THE INCLNE at constant spped,force due to gravitation is balanced by force due to friction.

so if friction constant is k,

then k*m*g*cos theta=m*g*sin theta

tan theta=k=0.325

now,when i send it upward,

total force=gravitational force+frictional force=2*m*g*sin 18

so acceleration=force/mass=2*g*sin 18=6.056 m/s^2 ,in downward direction

so if distance covered is d before coming to a halt:

then initial speed^2=2*deceleration*distance

d=0.33 m

c) no it wont slide back down..as static friction coefficeint is larger than dynamic friction coeffciient

so static friction will provide just enough force to balance the force due to gravitation.