A force F applied to an object of mass m1 produces an acceleration of 3.20 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 2.00 m/s2.
(a) What is the value of the ratio m1/m2?
(b) If m1 and m2 are combined, find their acceleration under the action of the force F.
m/s2
To find the value of the ratio m1/m2, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
For the first object:
F = m1 * a1
For the second object:
F = m2 * a2
Given that the force F is the same for both objects, we can set these two equations equal to each other:
m1 * a1 = m2 * a2
Now, let's substitute the given values:
3.20 m/s^2 * m1 = 2.00 m/s^2 * m2
Next, we can divide both sides of the equation by m2:
(3.20 m/s^2 * m1) / (2.00 m/s^2) = m2
Simplifying the equation further:
(m1 / 2.00 m/s^2) * 3.20 m/s^2 = m2
2.56 * m1 = m2
Now, we have the value of m1/m2 as 2.56. This is the answer to part (a).
For part (b), if m1 and m2 are combined, the total mass would be:
m_total = m1 + m2
To find the combined acceleration, we can again use Newton's second law of motion:
F = m_total * a_total
Since the force F remains the same, we can substitute it in:
F = (m1 + m2) * a_total
Rearranging the equation to solve for a_total:
a_total = F / (m1 + m2)
Now, we are given the force F and the values of m1 and m2. Plug in these values to calculate a_total:
a_total = F / (m1 + m2)
f=m1*a1
F=m2*a2
m1/m2 * a1/a2=1
m1/m1=a2/a1