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A force F with arrow applied to an object of mass m1 produces an acceleration of 3.10 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 1.80 m/s2.(a) What is the value of the ratio m1/m2?(b) If m1 and m2 are combined into one object, find its acceleration under the action of the force F with arrow.

Answer :

Answer:

(a) The value of the ratio m₁/m₂ is 0.581

(b)  the acceleration of the combined masses is 1.139 m/s²

Explanation:

Given;

The acceleration of force applied to M₁, a₁ = 3.10 m/s²

The same force applied to M₂ has acceleration, a₂ = 1.80 m/s²

Let this force = F

According Newton's second law of motion;

F = ma

(a) the value of the ratio m₁/m₂

since the applied force is same in both cases,  M₁a₁ = M₂a₂

[tex]\frac{m_1}{m_2} = \frac{a_2}{a_1} \\\\\frac{m_1}{m_2} = \frac{1.8}{3.1} \\\\\frac{m_1}{m_2} = 0.581[/tex]

(b) the acceleration of m₁ and m₂ combined as one object under the action force F

F = ma

[tex]a = \frac{F}{M} \\\\a = \frac{F}{m_1 + m_2} \\\\a = \frac{F}{0.581m_2 + m_2}\\\\a = \frac{F}{1.581m_2}[/tex]

[tex]But, m_2 = \frac{F}{a_2} \\\\a = \frac{F}{1.581m_2} = \frac{F*a_2}{1.581F} \\\\a = \frac{a_2}{1.581} \\\\a = \frac{1.8}{1.581} = 1.139 \ m/s^2[/tex]

Therefore, the acceleration of the combined masses is 1.139 m/s²

a. The value of the ratio is 0.581.

b. The acceleration should be [tex]1.139 m/s^2[/tex]

Newton's second law of motion:

Since

The acceleration of force applied to [tex]M_1,a_1 = 3.10 m/s^2[/tex]

The same force applied to[tex]M_2[/tex] has acceleration, [tex]a_2 = 1.80 m/s^2[/tex]

Here we assume force be F

Now we know that

F = ma

a. The ratio should be

[tex]m_1\div m_2 = a_2\div a_1\\\\m_1\div m_2 = 1.8\div 3.1[/tex]

= 0.581

b.  The acceleration should be

f = ma

a = F/m

[tex]a = f/m_1+m_2\\\\= F/0.581 + m_2\\\\=F/1.581m_2[/tex]

However [tex]m_2 = F/a_2[/tex]

So,

[tex]a = F\div 1.581m_2\\\\= f\times a_2/1.581F\\\\= a_2/1.581\\\\= 1.8/1.581\\\\= 1.139 m/s^2[/tex]

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