A very smart 3-year-old child is given a wagon for her birthday. She refuses to use it. "After all," she says, "Newton's third l
1 answer:
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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.
The graphs of the acceleration as a function of mass and of the acceleration as a function of force are in attachment.
Explanation:
To answer both parts of the question, we refer to Newton's second law, which states that:
where
F is the net force on an object
m is the mass of the object
a is its acceleration
a)
To answer this part, we re-arrange the previous equation as follows:
Therefore, we notice that if a constant force is applied, the acceleration is inversely proportional to the mass of the object:
this means that if the mass increases, the acceleration decreases, and if the mass decreases, the acceleration increases.
In a graph of acceleration vs mass, the curve representing this relationship would be a hyperbole. The graph is shown as the first graph in the attached picture.
b)
As before, we re-arrange the previous equation as follows:
Here we notice that if the object has a constant mass, the acceleration is directly proportional to the force applied on the object:
this means that when the force increases, the acceleration increases, and when the force decreases, the acceleration decreases.
In a graph of acceleration vs force, the curve representing this relationship would be a straight line, as shown in the second graph in the attached picture.
Learn more about Newton's second law of motion here:
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