Three objects with masses m1 = 36.3 kg, m2 = 17.7 kg, and m3 = 11.1 kg are hanging from ropes that are redirected over pulleys. What is the acceleration of m1? Negative numbers for downward, and positive numbers for upward, please.
are these masses somehow connected?
What is the magnitude of the net gravitational force on the m1=19kg mass in the figure?(Figure 1) Assume m2=m3=10kg.
To find the acceleration of m1, we need to analyze the forces acting on the system.
First, let's consider the forces acting on m1. There are two forces acting on it: the gravitational force (downward) and the tension force provided by the rope (upward). The magnitude of the gravitational force is given by m1 multiplied by the acceleration due to gravity (g), which is approximately 9.8 m/s².
The tension force is equal to the force needed to accelerate m1 upward. Let's denote this tension force as T1. Since the rope is redirected over a pulley, the tension force is equal on both sides of the pulley. Therefore, the tension force acting on m1 is also equal to the tension force acting on m2.
Next, let's consider the forces acting on m2. Similar to m1, there are two forces acting on m2: the gravitational force (downward) and the tension force (upward).
The tension force acting on m2 is the same as the tension force acting on m1. Let's denote this tension force as T2.
Finally, let's consider the forces acting on m3. Similarly, there are two forces acting on m3: the gravitational force (downward) and the tension force (upward).
The tension force acting on m3 is different from T1 and T2. Let's denote this tension force as T3.
Now, we can set up equations based on the forces acting on each object:
- For m1:
T1 - m1 * g = m1 * a
- For m2:
T2 - m2 * g = m2 * a
- For m3:
T3 - m3 * g = m3 * a
Since T1 = T2, we can combine the equations for m1 and m2:
T1 - m1 * g = m1 * a
T1 - m2 * g = m2 * a
Substituting T1 = T2 into the equations, we have:
T2 - m1 * g = m1 * a
T2 - m2 * g = m2 * a
We can solve this system of equations to find the value of a, the acceleration of m1.