Solving Force & Mass Ratios: Find m1/m2 & Acceleration

[bumblebeeliz]

Homework Statement

A force F applied to a mass m1 produces an acceleration of 3.0 m/s2. The same
force applied to a second object of mass m2 produces an acceleration of 1.0
m/s².

a. Find the value of the ratio m1 / m2.
b. If m1and m2 are combined, what will be the acceleration of the combined mass (m1+ m2) under the action of the force F?

Homework Equations

F=ma

The Attempt at a Solution

a)

I didn't know where to begin. So I chose a random number and assumed that my force was 6 N.

6N = m₁ a₁
6N = m₁ (3.0 m/s²)
6N / 3.0 m/s² = m₁
2 kg = m₁

6N = m₂ a₂
6N = m₁ (1.0 m/s²)
6N / 1.0 m/s² = m₂
6 kg = m₂

m₁/m₂ = 2kg/6kg = 0.333 = 3 x 10 ^-1

b)

F = (m₁+m₂) a
6N = (2kg + 6kg) a
6N / 8kg = a
0.75 m/s² = a

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Any suggestions? :)

 

[rock.freak667]

a)

I didn't know where to begin. So I chose a random number and assumed that my force was 6 N.

6N = m₁ a₁
6N = m₁ (3.0 m/s²)
6N / 3.0 m/s² = m₁
2 kg = m₁

6N = m₂ a₂
6N = m₁ (1.0 m/s²)
6N / 1.0 m/s² = m₂
6 kg = m₂

m₁/m₂ = 2kg/6kg = 0.333 = 3 x 10 ^-1

While this is correct. You didn't need to say F=6. It said the it applied the same force so F₁=F₂
or simply put m₁a₁=m₂a₂

b)
F = (m₁+m₂) a
6N = (2kg + 6kg) a
6N / 8kg = a
0.75 m/s² = a

---

Any suggestions? :)

So if F is the same, either F=m₁a₁ or F=m₂a₂


So you want F=(m₁+m₂)a . So you can put F equal to which either one you want and solve from there.

 

[bumblebeeliz]

Makes more sense! Thanks :)