Two block are connected by a lightweight, flexible cord that passes over friction less pulley. If m1=3.6 kg amd m2= 9.2kg, and block 2 is initially at rest 140 cm. above the floor, how long does it take block 2 to reach the floor?

net force pulling: g(m2-m1)

F=total mass*a
a= g(m2-m1)/(m2+m1)

d=1/2 a t^2 solve for t.

Why did the block go to the floor? Because it had a falling out with the cord!

Now, let's solve this problem. To find the time it takes for block 2 to reach the floor, we can use the principles of Newtonian mechanics and the concept of gravitational acceleration.

First, let's calculate the net force acting on the blocks. Since there is only one force acting on block 1 (its weight) and one force acting on block 2 (also its weight), we can write the following equations:

F_net1 = m1 * g (where g is the acceleration due to gravity)
F_net2 = m2 * g

We can assume the positive direction is downwards, so the equation for block 1 becomes:

F_net1 = m1 * g = -m1 * g (negative sign indicates upwards force)

Next, let's analyze the motion of the blocks. The force acting on block 1 will also be the tension in the cord since it is a lightweight, flexible cord with negligible weight. The net force on block 2 will be the weight of block 2 minus the tension in the cord, as it is moving downwards.

So we can write:

F_net1 = Tension
F_net2 = m2 * g - Tension

Since the blocks are connected by the cord, the tension in the cord is the same for both blocks. Hence, we can equate the two equations:

F_net1 = F_net2
-m1 * g = m2 * g - Tension

Rearranging the equation, we find:

Tension = (m2 + m1) * g

Now, we can determine the acceleration of block 2 using Newton's second law:

F_net2 = m2 * a
m2 * g - tension = m2 * a

Substituting the earlier equation for tension:

m2 * g - (m2 + m1) * g = m2 * a

Simplifying this equation gives us:

g * (m2 - m2 - m1) = m2 * a

m2 * a = -m1 * g

Finally, we can solve for the acceleration:

a = -m1 * g / m2

Plugging in the given values:

a = -(3.6 kg) * (9.8 m/s^2) / (9.2 kg)

Now that we have the acceleration, we can use the kinematic equation for motion in a vertical direction:

h = h0 + v0*t + (1/2)*a*t^2

Since the initial velocity of block 2 is zero and the final height is 0 cm, we can simplify the equation to:

0 = 140 cm + (1/2)*(-m1 * g / m2)*t^2

Simplifying further:

t^2 = (280 cm * m2) / (m1 * g)

Converting everything to SI units and calculating:

t^2 = (280 cm * 9.2 kg) / (3.6 kg * 9.8 m/s^2)

t^2 ≈ 7.103 s^2

Therefore, it takes approximately t = √7.103 ≈ 2.663 seconds for block 2 to reach the floor.

To find out how long it takes for block 2 to reach the floor, we need to calculate the acceleration of the system first using Newton's second law.

Step 1: Calculate the force of gravity acting on each block:
The force of gravity acting on block 1 is given by:
F1 = m1 * g
F1 = (3.6 kg) * (9.8 m/s^2)
F1 = 35.28 N

The force of gravity acting on block 2 is given by:
F2 = m2 * g
F2 = (9.2 kg) * (9.8 m/s^2)
F2 = 90.16 N

Step 2: Determine the net force acting on the system.
Since the cord is assumed to be lightweight and flexible, we can ignore its mass. The net force acting on the system is the difference in gravitational forces on the blocks:
Net Force = F2 - F1
Net Force = 90.16 N - 35.28 N
Net Force = 54.88 N

Step 3: Calculate the acceleration of the system.
Using Newton's second law, we can calculate the acceleration:
Net Force = mass * acceleration
54.88 N = (m1 + m2) * acceleration
54.88 N = (3.6 kg + 9.2 kg) * acceleration
54.88 N = 12.8 kg * acceleration
acceleration = 54.88 N / 12.8 kg
acceleration = 4.28 m/s^2

Step 4: Determine the time it takes for block 2 to reach the floor.
Using the kinematic equation, we can calculate the time it takes for block 2 to reach the floor:
Final velocity = initial velocity + (acceleration * time)
0 m/s = 0 m/s + (4.28 m/s^2 * time)
4.28 m/s^2 * time = 0 m/s
time = 0 seconds

Therefore, it takes 0 seconds for block 2 to reach the floor.

To find out how long it takes for block 2 to reach the floor, we can use the principles of Newton's laws of motion and the concept of conservation of energy.

Here's how you can calculate the time:

1. Determine the acceleration of the system:
- Since the system is connected by a lightweight, flexible cord passing over a frictionless pulley, the tension in the cord is the same on both sides.
- Applying Newton's second law to each block separately, we get:
- For block 1 (m1): m1 * a = m1 * g
- For block 2 (m2): m2 * a = m2 * g
- Here, g is the acceleration due to gravity (9.8 m/s^2).
- Since the acceleration is the same for both blocks, we can equate the two equations and solve for a.

2. Calculate the distance traveled by block 2:
- The distance traveled by block 2 is given as 140 cm (or 1.4 m) above the floor.

3. Use the kinematic equation to find the time taken to reach the floor:
- You can use the equation: s = u*t + (1/2)*a*t^2, where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time taken.
- Here, the initial velocity (u) for block 2 is 0 m/s since it starts from rest.

4. Substitute the values and solve for time:
- Plug in the values of the distance, acceleration (from step 1), and initial velocity into the kinematic equation.
- Rearrange the equation to solve for time (t).

Following these steps, you can calculate the time taken for block 2 to reach the floor.