Two blocks are connected by a lightweight, flexible cord that passes over a frictionless pulley. If mass one equals 3.6 Kg and mass two equals 9.2 Kg, and block two is initially at rest 140 cm above the floor, how Long does it take block two to reach the floor?
To find the time it takes for block two to reach the floor, we can use the principles of physics, specifically Newton's laws and the equations of motion.
In this scenario, we have two blocks connected by a cord passing over a frictionless pulley. The force of gravity acts on both blocks, causing them to accelerate as they move. The block with a mass of 3.6 kg is on the ground, and block two with a mass of 9.2 kg is initially at rest and 140 cm above the floor. We need to determine the time it takes for block two to reach the floor.
First, let's consider the forces acting on each block. Block one on the ground experiences the force of gravity pulling it downward with a magnitude equal to its weight, given by:
Weight of block one = mass of block one * acceleration due to gravity
= 3.6 kg * 9.8 m/s^2 (acceleration due to gravity)
= 35.28 N
Block two, initially at rest above the floor, also experiences the force of gravity pulling it downward. However, it has an additional force due to the tension in the cord, which opposes the force of gravity. This tension force is equal in magnitude to the weight of block one.
Now, let's examine the motion of block two. We can use Newton's second law to analyze the forces on block two:
Force_net = mass * acceleration
The net force acting on block two is the difference between the force of gravity and the tension in the cord:
Force_net = Force_gravity - Force_tension
The force of gravity on block two is given by:
Force_gravity = mass of block two * acceleration due to gravity
= 9.2 kg * 9.8 m/s^2
= 90.16 N
Since the tension in the cord is equal to the weight of block one (35.28 N), we can substitute these values into the equation for the net force:
Force_net = 90.16 N - 35.28 N
= 54.88 N
Now, we can use Newton's second law to solve for the acceleration of block two:
Force_net = mass of block two * acceleration
54.88 N = 9.2 kg * acceleration
acceleration = 5.97 m/s^2
With the acceleration known, we can use the kinematic equation to determine the time it takes for block two to reach the floor. Assuming block two starts from rest:
s = ut + (1/2)at^2
Since the block starts from rest, its initial velocity (u) is 0. The distance (s) travelled by block two is 140 cm or 1.4 m. Substituting the values into the equation:
1.4 = (1/2)(5.97)t^2
2.8 = 5.97t^2
t^2 = 2.8 / 5.97
t^2 = 0.468
t = sqrt(0.468)
t = 0.685 s
Therefore, it takes approximately 0.685 seconds for block two to reach the floor.