What is the relationship between mass and gravitational force between any two objects?
1 answer:
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Answer:
The moment of inertia I is
I = 2.205x10^-4 kg/m^2
Explanation:
Given mass m = 0.5 kg
And side lenght = 0.03 m
Moment of inertia I = mass x radius of rotation squared
I = mr^2
In this case, the radius of rotation is about an axis which is both normal (perpendicular) to and through the center of a face of the cube.
Calculating from the dimensions of the the box as shown in the image below, the radius of rotation r = 0.021 m
Therefore,
I = 0.5 x 0.021^2 = 2.205x10^-4 kg/m^2
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.
