A horizontal forces of magnitude 500N pulls two blocks of masses m1=10 kg and m2=20 kg which are connected by the light inextensible string and lying on the horizontal frictionless surface. Find the tension in the strings and acceleration of each mass when forces is applied on mass
m2?
t=166
To find the tension in the strings and the acceleration of each mass, we can use Newton's Second Law of Motion, which states that the net force on an object is equal to the product of its mass and acceleration.
Here are the step-by-step calculations:
Step 1: Calculate the net force acting on the system.
Since the only horizontal force acting on the system is the applied force on m2, the net force on the system is equal to the applied force.
Net Force = Applied Force = 500 N
Step 2: Determine the acceleration of the system.
Using Newton's Second Law, we can find the acceleration of the system.
Net Force = (m1 + m2) * acceleration
500 N = (10 kg + 20 kg) * acceleration
500 N = 30 kg * acceleration
Solving for acceleration:
acceleration = 500 N / 30 kg
acceleration ≈ 16.67 m/s^2
Step 3: Calculate the tension in the string.
Since the system is connected by a light inextensible string, the tension in the string will be the same on both sides.
Tension = m2 * acceleration = 20 kg * 16.67 m/s^2
Tension ≈ 333.33 N
Therefore, the tension in the strings is approximately 333.33 N, and the acceleration of each mass is approximately 16.67 m/s^2.
To find the tension in the strings and the acceleration of each mass when a force is applied to mass m2, we can use Newton's second law of motion, which states that the net force applied to an object is equal to the mass of the object multiplied by its acceleration.
Step 1: Determine the net force applied to the system:
Since only a force is applied to mass m2, the net force acting on the system is the force applied to m2. In this case, the force applied to m2 is 500N.
Step 2: Calculate the acceleration of the system:
To find the acceleration of the system, we need to consider the individual forces acting on each block. The force applied to mass m2 will accelerate it, while the tension in the string will provide the opposing force. The tension in the string will also transmit to mass m1, accelerating it as well.
The net force on m2 can be written as:
Net Force on m2 = Force Applied to m2 - Tension in string
Thus, the equation becomes:
m2 * acceleration = Force Applied to m2 - Tension in string (equation 1)
The net force on m1 can be written as:
Net Force on m1 = Tension in string
Thus, the equation becomes:
m1 * acceleration = Tension in string (equation 2)
Step 3: Solve the system of equations:
We have two equations and two unknowns (tension in the string and the acceleration), so we can solve the system of equations simultaneously.
Using equation 1, we can express the tension in the string as:
Tension in string = Force Applied to m2 - m2 * acceleration
Substitute this value into equation 2:
m1 * acceleration = Force Applied to m2 - m2 * acceleration
Now, we can solve for acceleration:
m1 * acceleration + m2 * acceleration = Force Applied to m2
( m1 + m2 ) * acceleration = Force Applied to m2
acceleration = Force Applied to m2 / ( m1 + m2 )
To find the tension in the string, substitute the acceleration value back into equation 1:
Tension in string = Force Applied to m2 - m2 * acceleration
Finally, substitute the given values of m1, m2, and the force applied to m2 into the equations to calculate the tension in the string and the acceleration.