a = 1.5 m/s^2 , down the plane.
t = 5.2 s to reach bottom.
So, a total of t = 5.6 s for the block to go up and back down.Step-by-Step Solution to #1:
Step 1: Free-body diagram:
Step 2: Break vectors into components. Because we have an incline, we use inclined axes, one parallel
and one perpendicular to the incline:
Step 3: Write Newton’s second law for each axis. The acceleration is entirely directed parallel to the
plane, so perpendicular acceleration can be written as zero:
mg sin θ − 0 = ma .F (^) N − mg cos θ = 0.
Step 4: Solve algebraically for a . This can be done without reference to the second equation. (In
problems with friction, use F (^) f = μF (^) N to relate the two equations.)
a = g sin θ = 6.3 m/s^2