Q- Three objects are connected by two very light, flexible, and unstretchable string as shown in the figure, where M=9 kg and m=2.5 kg. You can ignore friction and the mass of the pulley. When the objects are released;
(a) Calculate the magnitude of the acceleration (in m/s2) of each object.
(b) Calculate the tension T1 (in N) in the string.
(c) Calculate the tension T2 (in N) in the string.
To answer these questions, we need to analyze the forces acting on the objects and apply Newton's laws of motion.
First, let's consider the motion of the 9 kg object (M). We'll call the acceleration of this object "a1."
(a) To calculate the magnitude of the acceleration of the 9 kg object (M), we'll apply Newton's second law: F = ma.
The only force acting on M is the tension force T1 in the string pulling M upwards. So we have:
T1 - mg = Ma1
Here, g represents the acceleration due to gravity (approximately 9.8 m/s^2). The mass of object M is 9 kg.
Rearranging the equation, we have:
T1 = Ma1 + mg
Substituting the values, we get:
T1 = (9 kg)(a1) + (9 kg)(9.8 m/s^2)
Now, let's consider the motion of the 2.5 kg object (m). We'll call the acceleration of this object "a2."
(b) To calculate the tension T1 in the string, we'll apply Newton's second law to the 2.5 kg object (m):
T2 - mg = ma2
Here, the force acting on m is the tension T2 in the string, which pulls m downwards. The mass of object m is 2.5 kg.
Rearranging the equation, we have:
T2 = ma2 + mg
Now, let's consider the motion of the pulley. Since the pulley is light and unstretchable, it doesn't contribute to the gravitational forces on the objects.
(c) To calculate the tension T2 in the string, we'll use the fact that the string is unstretchable. This means that the tension in the string on both sides of the pulley must be equal.
So, T1 = T2.
Now, we have two equations:
T1 = (9 kg)(a1) + (9 kg)(9.8 m/s^2)
T2 = (2.5 kg)(a2) + (2.5 kg)(9.8 m/s^2)
We need to solve these equations simultaneously to find the values of a1, a2, T1, and T2.
This requires a bit more information about the precise configuration of the system, like the angle at which the strings are attached to the objects or any other relevant information. Please provide any additional details, and I'll guide you on how to solve the problem further.