Two bodies of mass 3kg and 4kg are suspended at the ends of massless string passing over a frictionless pulley .the acceleration system is
1 kg * g = (3+4) a
a = g/5
a=g/7
=1.4m/sq sec
To find the acceleration of the system, we need to apply Newton's second law of motion, which states that the net force on an object is equal to the mass of the object times its acceleration.
In this case, the net force on the system is the difference between the forces exerted by the two masses. Let's assume that the 3 kg mass is on the left side and the 4 kg mass is on the right side. The force exerted by the 3 kg mass is given by:
F1 = m1 * g
Where m1 is the mass of the 3 kg mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Similarly, the force exerted by the 4 kg mass is given by:
F2 = m2 * g
Where m2 is the mass of the 4 kg mass.
Since the masses are connected by a massless string passing over a frictionless pulley, the tension in the string is the same on both sides. Therefore, we can equate the forces:
F1 = F2
m1 * g = m2 * g
Simplifying this equation, we find:
m1 = m2
Thus, the masses cancel out and the acceleration of the system can be calculated using the following equation:
a = (m1 - m2) * g / (m1 + m2)
Plugging in the values, we get:
a = (3 kg - 4 kg) * 9.8 m/s^2 / (3 kg + 4 kg)
a = -1 kg * 9.8 m/s^2 / 7 kg
a ≈ -1.4 m/s^2
Note that the negative sign indicates that the acceleration is in the opposite direction of our assumed positive direction. Therefore, the system accelerates towards the 3 kg mass.
To find the acceleration of the system, we can use Newton's second law of motion.
First, we need to determine the net force acting on the system. Since there is an upward force due to the tension in the string and a downward force due to the weight of the masses, we can write the equation:
Net Force = Tension - Weight
The weight of an object can be calculated using the formula:
Weight = mass * gravity
Where mass is the mass of the object and gravity is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
For the 3 kg mass:
Weight1 = 3 kg * 9.8 m/s^2
For the 4 kg mass:
Weight2 = 4 kg * 9.8 m/s^2
Now, we can calculate the net force:
Net Force = Tension - (Weight1 + Weight2)
From Newton's second law, we know that the net force is equal to the mass of the system multiplied by the acceleration:
Net Force = (mass1 + mass2) * acceleration
Setting up the equation, we have:
(mass1 + mass2) * acceleration = Tension - (Weight1 + Weight2)
Simplifying the equation, we have:
(mass1 + mass2) * acceleration = Tension - (mass1 * gravity + mass2 * gravity)
Now, we need to consider the tension in the string. Since the masses are connected by a massless string, the tension acting on both sides of the pulley has to be the same. Let's denote the tension as T.
The downward tension on the 3 kg mass is T, and the upward tension on the 4 kg mass is also T. Therefore, the net force equation becomes:
(mass1 + mass2) * acceleration = T - (mass1 * gravity + mass2 * gravity)
Combining like terms, we get:
(3 kg + 4 kg) * acceleration = T - (3 kg * 9.8 m/s^2 + 4 kg * 9.8 m/s^2)
Now, we know that the mass of the system is simply the sum of the individual masses:
(7 kg) * acceleration = T - (3 kg * 9.8 m/s^2 + 4 kg * 9.8 m/s^2)
Finally, to find the acceleration of the system, we divide both sides of the equation by the total mass:
acceleration = (T - (3 kg * 9.8 m/s^2 + 4 kg * 9.8 m/s^2)) / (7 kg)