Three objects are connected as shown in the figure below. They move along a horizontal, frictionless surface, and are pulled to the right with a force Fext = 2.4 N. With the three mass values given as m1 = 604 g, m2 = 744 g, and m3 = 693 g. Calculate the magnitude of the acceleration of the three objects.
The description is inadequate, I have no idea how the objects are connected.
If they are in a line, a=force/total mass.
To calculate the magnitude of acceleration of the three objects, we need to apply Newton's second law of motion, which states that the acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass. The equation is:
Fnet = ma
where Fnet is the net force, m is the mass of the object, and a is the acceleration.
In this case, the force acting on the three objects is the external force, Fext = 2.4 N, which is pulling them to the right.
For object 1, the net force acting on it is the force pulling it to the right (Fext) minus the force exerted by object 2 (m2) and object 3 (m3). So, the net force acting on object 1 is:
F1net = Fext - F2 - F3
F2 = m2 * a, and F3 = m3 * a
Substituting these values into the equation:
F1net = Fext - m2 * a - m3 * a
Similarly, for object 2, the net force acting on it is the force pulling it to the right (Fext) minus the force exerted by object 1 (m1) and object 3 (m3). So, the net force acting on object 2 is:
F2net = Fext - F1 - F3
F1 = m1 * a, and F3 = m3 * a
Substituting these values into the equation:
F2net = Fext - m1 * a - m3 * a
Finally, for object 3, the net force acting on it is the force pulling it to the right (Fext) minus the force exerted by object 1 (m1) and object 2 (m2). So, the net force acting on object 3 is:
F3net = Fext - F1 - F2
F1 = m1 * a, and F2 = m2 * a
Substituting these values into the equation:
F3net = Fext - m1 * a - m2 * a
Since the net force acting on each object is the same (Fext), we can set up an equation:
Fext - m2 * a - m3 * a = Fext - m1 * a - m3 * a = Fext - m1 * a - m2 * a
Simplifying the equation:
Fext - m2 * a - m3 * a = Fext - m1 * a - m3 * a
-m2 * a = -m1 * a
Dividing both sides of the equation by -a:
m2 = m1
This tells us that the magnitudes of the acceleration for objects 1, 2, and 3 are equal.
Therefore, the magnitude of acceleration of the three objects is the same and can be calculated by considering only one of the objects.
Let's use object 1 to calculate the acceleration.
F1net = Fext - F2 - F3
F1net = 2.4 N - m2 * a - m3 * a
m1 * a = 2.4 N - m2 * a - m3 * a
m1 * a = 2.4 N - (m2 + m3) * a
a * (m1 + m2 + m3) = 2.4 N
a = 2.4 N / (m1 + m2 + m3)
Now we can plug in the values:
m1 = 604 g = 0.604 kg
m2 = 744 g = 0.744 kg
m3 = 693 g = 0.693 kg
a = 2.4 N / (0.604 kg + 0.744 kg + 0.693 kg)
a = 2.4 N / 2.041 kg
a ≈ 1.177 m/s²
Therefore, the magnitude of acceleration of the three objects is approximately 1.177 m/s².