Need help with question after number 40
1 answer:
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Answer:
i) No, the spring scale does not read a different value
ii) The torque will read a different value, it will reduce
iii) The spring scale does not need to be measured at the center of mass location.
Explanation:
The torque caused by the gyroscope can be given by the relation,
r × f
The torque measured by the gyroscope varies directly with the distance, r.
A decrease in the distance r will also cause a decrease in the value of the torque measured. When the distance, r is reduced from 7.5 inches to 5 inches, the torque caused by the gyroscope's weight also reduces.
The weight of the gyroscope remains constant despite the reduction in the distance because the weight of the gyroscope is not a function of the distance from the gyroscope. Therefore, the spring scale will not read a different value.
Yes, the spring scale does not need to be measured from the center of mass location because the weight does not depend on the location of measurement. The reading of the sprig scale remains constant.
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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