a mass of 3kg rests on smooth horizontal table connected by a light string passion over a smooth pulley at the edge of the table to another mass of 2kg hanging vertically. when the system is released from rest with what acceleration do the masses move and what is the tension in the string g=10metre per seconds square
To find the acceleration of the masses and the tension in the string, we can apply Newton's second law of motion to each individual mass.
Let's start with the mass of 3 kg on the horizontal table. Since it is connected to a mass hanging vertically, the tension in the string is the force that will accelerate the horizontal mass.
For the horizontal mass (3 kg):
- The net force acting on it is the tension force applied by the string.
- According to Newton's second law, the net force can be calculated by multiplying mass with acceleration: net force = mass * acceleration. In this case, mass = 3 kg.
- The acceleration of the horizontal mass can be considered as the same for the hanging mass.
- Since the table is smooth, there is no friction, so the net force is equal to the tension force.
For the hanging mass (2 kg):
- The force acting on it is the force due to gravity, which can be calculated as mass * gravitational acceleration. In this case, mass = 2 kg and gravitational acceleration (g) = 10 m/s².
- Since the mass hangs freely, the tension force in the string is equal to the gravitational force acting on it.
Now, we can set up the equations to find the acceleration and tension:
1. For the horizontal mass:
net force = tension force = (3 kg) * acceleration.
2. For the hanging mass:
tension force = gravitational force = (2 kg) * (10 m/s²).
Since the tension force is the same for both masses, we have:
(3 kg) * acceleration = (2 kg) * (10 m/s²).
Simplifying the equation:
3 * acceleration = 2 * 10,
3 * acceleration = 20,
acceleration = 20 / 3 ≈ 6.67 m/s².
Therefore, the masses will move with an acceleration of approximately 6.67 m/s². To find the tension in the string, we substitute this acceleration into one of the equations. Let's use the equation for the horizontal mass:
tension force = (3 kg) * (6.67 m/s²) ≈ 20.01 N.
Thus, the tension in the string is approximately 20.01 Newtons.
To find the acceleration and tension in the string, we can use Newton's second law of motion.
Let's consider the two masses in this system: 3kg and 2kg.
For the 3kg mass on the table:
The force acting on it is the tension in the string, which we'll call T1.
Using Newton's second law, F = ma, where F is the force, m is the mass, and a is the acceleration.
Since the mass is on a smooth table, there is no friction, so the only force acting on it is the tension.
Therefore, we have T1 = m₁ * a, where m₁ = 3kg.
For the 2kg mass hanging vertically:
The force acting on it is the weight, which is given by the equation F = mg, where m is the mass and g is the acceleration due to gravity.
So, the weight of the 2kg mass is F = m₂ * g = 2kg * (10m/s²) = 20N.
Since the system is released from rest, the acceleration of the 2kg mass is equal to the system's acceleration. Let's call it a.
Now, we consider the tension in the string, T2, which is acting against the weight of the 2kg mass.
The net force on the 2kg mass is T2 - F = m₂ * a, where m₂ = 2kg.
Substituting the values, we get T2 - 20N = 2kg * a.
Since the two masses are connected by the same string, the tensions in the string are equal and opposite, so T1 = T2.
Hence, we have T1 = T2 = T.
Now, we can solve the equations:
For the 3kg mass: T = 3kg * a
For the 2kg mass: T - 20N = 2kg * a
Since T1 = T2 = T, we can equate the two equations:
3kg * a = T - 20N
Substituting T = 3kg * a into the equation, we get:
3kg * a = 3kg * a - 20N
Simplifying the equation, we find that -20N = 0.
Since this equation doesn't have any solution, it means that the system will not move.
F=ma
the tension in the string is the downward weight of the 2kg mass.
The force on the 3kg mass is that weight.