A certain force gives mass m1 an acceleration of 10.0 m/s2 and mass m2 an acceleration of 4.0 m/s2. What acceleration would the force give to an object with a mass of (m2-m1)?
To find the acceleration of an object with a mass of (m2 - m1), we can use Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration.
Given that the force gives mass m1 an acceleration of 10.0 m/s^2 and mass m2 an acceleration of 4.0 m/s^2, we can set up two equations:
F = m1 * a1 (Equation 1)
F = m2 * a2 (Equation 2)
Since the force applied (F) is the same in both scenarios, we can equate Equations 1 and 2:
m1 * a1 = m2 * a2
Now, let's substitute a1 = 10.0 m/s^2 and a2 = 4.0 m/s^2 into the equation:
m1 * 10.0 m/s^2 = m2 * 4.0 m/s^2
Next, we want to find the acceleration that the force would give to an object with a mass of (m2 - m1). Let's substitute (m2 - m1) for one of the masses in the equation, assuming we let (m2 - m1) be the mass of the object with the unknown acceleration:
(m2 - m1) * a = m2 * 4.0 m/s^2
Now, let's solve this equation for the unknown acceleration (a). We'll start by expanding the left side of the equation:
(m2 - m1) * a = (m2 * a) - (m1 * a)
Next, we isolate the unknown acceleration (a) by moving the term (m1 * a) to the other side:
(m2 - m1) * a + (m1 * a) = m2 * 4.0 m/s^2
Factoring out 'a' on the left side of the equation:
(a * (m2 - m1 + m1)) = m2 * 4.0 m/s^2
Simplifying:
a * m2 = m2 * 4.0 m/s^2
Finally, we can divide both sides of the equation by m2 to solve for 'a':
a = (m2 * 4.0 m/s^2) / m2
Simplifying further:
a = 4.0 m/s^2
Therefore, the acceleration that the force would give to an object with a mass of (m2 - m1) is 4.0 m/s^2.