A force F applied to an object of mass m, produces an acceleration of 3.90 m/s². The same force applied to a second object of mass m, produces an acceleration of 1.70 m/s. (a) What is the value of the ratio m./m,? 23 Be very careful in setting up ratios. Write down the relationships explicitly and do the algebra to obtain the proportionality. (b) If m, and m, are combined into one object, find its acceleration under the action of the force F. 1.16 Write equations relating F, m, and a for the three cases (m m, and m) and then manipulate the equation to determine the acceleration of the sum in terms of the other two accelerations. m/s? Need Help? Read It Watch it

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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**Physics Problem Example**

**Scenario:**

A force \( F \) applied to an object of mass \( m_1 \) produces an acceleration of \( 3.90 \, \text{m/s}^2 \). The same force applied to a second object of mass \( m_2 \) produces an acceleration of \( 1.70 \, \text{m/s}^2 \). 

**Questions:**

**(a)** What is the value of the ratio \( m_1/m_2 \)?

- Incorrect attempt: \( 2.3 \)

*Note:* Be very careful in setting up ratios. Write down the relationships explicitly and do the algebra to obtain the proportionality.

**(b)** If \( m_1 \) and \( m_2 \) are combined into one object, find its acceleration under the action of the force \( F \).

- Incorrect attempt: \( 1.16 \)

*Note:* Write equations relating \( F, m, \) and \( a \) for the three cases (\( m_1, m_2, \text{and } m_{\text{sum}} \)) and then manipulate the equation to determine the acceleration of the sum in terms of the other two accelerations, \( \text{m/s}^2 \).

For assistance, use the resources available to you, such as "Read It" or "Watch It" help options.
Transcribed Image Text:**Physics Problem Example** **Scenario:** A force \( F \) applied to an object of mass \( m_1 \) produces an acceleration of \( 3.90 \, \text{m/s}^2 \). The same force applied to a second object of mass \( m_2 \) produces an acceleration of \( 1.70 \, \text{m/s}^2 \). **Questions:** **(a)** What is the value of the ratio \( m_1/m_2 \)? - Incorrect attempt: \( 2.3 \) *Note:* Be very careful in setting up ratios. Write down the relationships explicitly and do the algebra to obtain the proportionality. **(b)** If \( m_1 \) and \( m_2 \) are combined into one object, find its acceleration under the action of the force \( F \). - Incorrect attempt: \( 1.16 \) *Note:* Write equations relating \( F, m, \) and \( a \) for the three cases (\( m_1, m_2, \text{and } m_{\text{sum}} \)) and then manipulate the equation to determine the acceleration of the sum in terms of the other two accelerations, \( \text{m/s}^2 \). For assistance, use the resources available to you, such as "Read It" or "Watch It" help options.
Expert Solution
Step 1

Using newton's second law of motion :

F = ma

Since force is same for both the masses ,

Therefore :

m1 a1 = m2 a2

m(3.9) = m2 (1.7)

m1 / m2 = (1.7/3.9)

 = 0.436

 

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