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A constant force applied to object A causes it to
Chapter 5, Problem 6CQ(choose chapter or problem)
A constant force applied to \(\mathrm{A}\) causes \(\mathrm{A}\) to accelerate at \(5 \mathrm{~m} / \mathrm{s}^{2}\). The same force applied to \(\mathrm{B}\) causes an acceleration of \(3 \mathrm{~m} / \mathrm{s}^{2}\). Applied to \(\mathrm{C}\), it causes an acceleration of \(8 \mathrm{~m} / \mathrm{s}^{2}\).
a. Which object has the largest mass? Explain.
b. Which object has the smallest mass?
c. What is the ratio \(m_{\mathrm{A}} / m_{\mathrm{B}}\) of the mass of \(\mathrm{A}\) to the mass of \(\mathrm{B}\)?
Equation Transcription:
Text Transcription:
A
A
5 m/s^2
B
3 m/s^2
C
8 m/s^2
m_A/m_B
A
B
Questions & Answers
QUESTION:
A constant force applied to \(\mathrm{A}\) causes \(\mathrm{A}\) to accelerate at \(5 \mathrm{~m} / \mathrm{s}^{2}\). The same force applied to \(\mathrm{B}\) causes an acceleration of \(3 \mathrm{~m} / \mathrm{s}^{2}\). Applied to \(\mathrm{C}\), it causes an acceleration of \(8 \mathrm{~m} / \mathrm{s}^{2}\).
a. Which object has the largest mass? Explain.
b. Which object has the smallest mass?
c. What is the ratio \(m_{\mathrm{A}} / m_{\mathrm{B}}\) of the mass of \(\mathrm{A}\) to the mass of \(\mathrm{B}\)?
Equation Transcription:
Text Transcription:
A
A
5 m/s^2
B
3 m/s^2
C
8 m/s^2
m_A/m_B
A
B
Step 1 of 3
(a)
Our aim is to find the object that has the largest mass for the given acceleration and the constant force.
The acceleration on object \(\mathrm{A} \mathrm{a}_{\mathrm{A}}=5 \mathrm{~m} / \mathrm{s}^{2}\)
The acceleration on object \(\mathrm{B} \mathrm{a}_{\mathrm{B}}=3 \mathrm{~m} / \mathrm{s}^{2}\)
The acceleration on object \(\mathrm{C} \mathrm{a}_{\mathrm{A}}=8 \mathrm{~m} / \mathrm{s}^{2}\)
The force applied is assumed to be \(F\)
In the case of constant force, the acceleration (a) is given by
\(a \propto \frac{1}{m}\)
Since the acceleration is inversely proportional to the mass, the object that accelerated minimum acceleration will have the largest mass.
The answer is the object \(\mathrm{B}\).