A 72 N force accelerates mass m1 by 5.0 m/s^2. The same force acts on another mass m2. What acceleration will the same force impart to the two masses when they are joined together?

F = ma, so a = F/m

a1 = 72/m1
a2 = 72/(m1+m2)

not sure whether the "same force" means the same 72N force, or another force of equal size.

If the latter, then both forces acting together would impart an acceleration of

(72+72)/(m1+m2)

Answer

To find the acceleration when the two masses are joined together, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass.

Let's denote the mass of the first object as m1 and the mass of the second object as m2. The force acting on both objects is the same, given as 72 N. The acceleration of the first object, when the force is applied to it, is 5.0 m/s^2.

According to Newton's second law, for the first object:
F = m1 * a1,
where F is the force, m1 is the mass of the first object, and a1 is the acceleration of the first object.

To find the acceleration of the second object, we can use the same force applied to both objects joined together. Let's call this acceleration a2.

For the second object:
F = m2 * a2.

Since the force acting on both objects is the same, we can equate the two equations:
m1 * a1 = m2 * a2.

Now, let's rearrange the equation to solve for a2:
a2 = (m1 * a1) / m2.

Substituting the known values, we have:
a2 = (m1 * 5.0 m/s^2) / m2.

Therefore, the acceleration when the two masses are joined together is (m1 * 5.0 m/s^2) / m2.