Answer:
A: The acceleration is 7.7 m/s up the inclined plane.
B: It will take the block 0.36 seconds to move 0.5 meters up along the inclined plane
Explanation:
Let us work with variables and set
As shown in the attached free body diagram, we choose our coordinates such that the x-axis is parallel to the inclined plane and the y-axis is perpendicular. We do this because it greatly simplifies our calculations.
Part A:
From the free body diagram we see that the total force along the x-axis is:
Now the force of friction is where
is the normal force and from the diagram it is
Thus
Therefore,
Substituting the value for we get:
Now acceleration is simply
The negative sign indicates that the acceleration is directed up the incline.
Part B:
Which can be rearranged to solve for t:
Substitute the value of and
and we get:
which is our answer.
Notice that in using the formula to calculate time we used the positive value of , because for this formula absolute value is needed.
