Two Blocks, Massless Rope. Pulley

In summary, the problem involves two blocks connected by a rope over a pulley, with one block weighing 3.3 kg and the other weighing 4.2 kg. The pulley has a diameter of 12 cm and a mass of 2.0 kg, and there is a torque of 0.35 Nm due to friction at the axle. The goal is to determine the time it takes for the 4.2 kg block to reach the floor from a height of 1.0 m. To solve this, the equations for force and torque are used for each mass and the pulley, with the assumption that the accelerations of the two masses are equal but in opposite directions. This results in three
  • #1
kls5010
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Homework Statement



The two blocks, m1 = 3.3 kg and m2 = 4.2, in the figure below are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.35 Nm. If the blocks are released from rest, how long does it take the 4.2 kg block to reach the floor from a height of h = 1.0 m?


Homework Equations



torque= r * F
sum of torques = moment of inertia * angular acceleartion
angular acceleration * radius = acceleration
x=v0t + 1/2 a t^2



The Attempt at a Solution



I tried summing torques, saying that m2 is on the left and has torque m2*g*radius. Following this, m1 acts opposite, so subtract m1*g*radius. Friction acts opposite of motion, so acts the direction of m1. So (m2*g*r) - (m1*g*r) - torque(friction) = alpha * 1/2m*r^2 (m is mass of pulley, r is .06m, m1 = 3.3, m2=4.2)

from here, i used alpha*r=a to find linear acceleration

then i used x=v0t + 1/2at^2 to find time, v0 is 0 because it starts at rest, a is what i found before

Any suggestions?
 
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  • #2
You need to examine each part separately... the mass on one end of the pulley... the mass on the other end... and the pulley itself...

Write the f = ma equations for each of the 2 masses...

Write the torque = I*alpha equation for the pulley...

The two tensions cannot be assumed to be the same... so assume two variables T1 and T2...

The acceleration of one mass upward will equal the acceleration of the other mass downward.

alpha = a/0.06

you'll have 3 equations with 3 unknowns. a, T1, T2...
 
  • #3


As a scientist, it is important to first identify the relevant equations and variables in the problem. In this case, we have two blocks connected by a massless rope over a pulley. The pulley has a mass and friction at its axle is given. The problem asks for the time it takes for the 4.2 kg block to reach the floor from a height of 1.0 m.

To solve this problem, we can start by considering the forces acting on each block. The 3.3 kg block will experience a downward force due to gravity (m1*g) and a tension force from the rope (T). The 4.2 kg block will also experience a downward force due to gravity (m2*g) and a tension force from the rope (T). The direction of the tension force will be opposite for each block due to the direction of motion.

Next, we can consider the pulley. The friction at the axle will exert a torque in the opposite direction of motion, as stated in the problem. This torque can be calculated using the equation torque = radius * force. We can also calculate the moment of inertia of the pulley using the equation moment of inertia = 1/2 * mass * radius^2.

Now, we can use the equation sum of torques = moment of inertia * angular acceleration to determine the angular acceleration of the pulley. We can then use the equation angular acceleration * radius = linear acceleration to find the linear acceleration of the blocks.

Finally, we can use the equation x = v0t + 1/2at^2 to find the time it takes for the 4.2 kg block to reach the floor. We know that the initial velocity (v0) is 0 m/s since the block starts at rest, and we can use the linear acceleration we calculated earlier.

It is important to remember to use consistent units throughout the problem and to double check all calculations. If you encounter any difficulties, it may be helpful to draw a free-body diagram and label all forces and directions.
 

What is the concept of "Two Blocks, Massless Rope, Pulley"?

The concept of "Two Blocks, Massless Rope, Pulley" is a common problem in introductory physics that involves two blocks connected by a massless rope that runs over a pulley. This setup allows for the study of concepts such as tension, forces, and acceleration.

What are the assumptions made in this setup?

There are a few assumptions made in this setup, including the assumption that the rope is massless, the pulley is frictionless, and the blocks are in contact with a frictionless surface. These assumptions allow for the simplification of the problem and make it easier to analyze.

How do you calculate the tension in the rope?

The tension in the rope can be calculated using Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this setup, the tension in the rope is equal to the mass of the blocks multiplied by the acceleration of the system.

What is the relationship between the two blocks in this setup?

In this setup, the two blocks are connected by a massless rope, which means that they move together and have the same acceleration. Additionally, the tension in the rope is the same on both sides of the pulley, as the rope is assumed to be massless.

How does the acceleration of the system depend on the masses of the blocks?

The acceleration of the system depends on the masses of the blocks, as shown by Newton's second law. The heavier block will experience a larger force and thus a larger acceleration, while the lighter block will experience a smaller force and a smaller acceleration. However, the acceleration of the system as a whole will be the same, as the two blocks are connected by a massless rope.

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