Newtons Law Problem: objects and pulleys

In summary, the problem involves three blocks connected by cords over frictionless pulleys, with masses of 6kg, 8kg, and 10kg respectively. Block B is on a frictionless table, while blocks A and C hang off the left and right sides. The question asks for the tension in the cord at the right when the blocks are released. To solve this, we can use the equations F=ma and Tension force= mgcos0, but since no angles are given, we cannot proceed with the solution. If angles had been given, we could set up equations such as F=ma and Tension force= mgcosθ, where θ is the angle of the cord. However, without this information
  • #1
wegman14
8
0

Homework Statement


three blocks attatched by cords that loop over frictionless pulleys. Block B lies on frictionless table, block a hangs off the left side of the table, while block c hangs off the right side. mass a= 6kg mass b= 8kg and mass c= 10kg. When the blocks are released, what is the tension in the cord at the right?


Homework Equations


F=ma
Tension force= mgcos0

The Attempt at a Solution


i don't really have an attempt at the solution, i don't see where to go when only given the masses of the objects. Also, there is no angles involved so it eliminates some of my equations
 
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  • #2
wegman14 said:

The Attempt at a Solution


i don't really have an attempt at the solution, i don't see where to go when only given the masses of the objects. Also, there is no angles involved so it eliminates some of my equations

What else do you feel you need apart from the masses to proceed toward a solution? If angles had been given, how would you have set up the equations? Give an example, so that we can consider it further.
 
  • #3
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As a scientist, let me guide you through the problem-solving process for this question. First, let's draw a free body diagram for each block, showing all the forces acting on them. For block A, we have the force of gravity (mg) pulling it down and the tension force (T) pulling it up. For block B, we have the force of gravity pulling it down and the normal force (N) pushing it up. For block C, we have the force of gravity pulling it down and the tension force pulling it up.

Next, let's apply Newton's Second Law (F=ma) to each block. For block A, we have Fnet = T - mg = ma. Since the block is hanging at rest, its acceleration is zero, so we can solve for T: T = mg. This means that the tension in the cord on the left side is equal to the weight of the block (6kg * 9.8m/s^2 = 58.8N).

For block B, we have Fnet = N - mg = ma. Again, since the block is at rest, its acceleration is zero, so we can solve for N: N = mg. This means that the normal force pushing up on the block is equal to its weight (8kg * 9.8m/s^2 = 78.4N).

For block C, we have Fnet = T - mg = ma. Since the block is accelerating downwards, we can solve for T: T = mg + ma. Here, we need to use the mass and acceleration of the entire system, not just block C. We know that the total mass of the system is 24kg (6kg + 8kg + 10kg) and the total acceleration is 9.8m/s^2 (since all blocks are accelerating downwards due to gravity). Plugging these values in, we get T = (24kg * 9.8m/s^2) + (24kg * 9.8m/s^2) = 470.4N. This is the tension in the cord on the right side.

In summary, the tension in the cord on the right side is 470.4N. It is important to draw free body diagrams and apply Newton's Laws to each block separately in order to solve complex problems like this one. Also, keep in mind that the masses and accelerations of the
 

1. What are Newton's Laws of Motion?

Newton's Laws of Motion are three fundamental principles that describe the behavior of objects in motion. These laws were developed by Sir Isaac Newton in the 17th century and are still used today to understand and explain the motion of objects.

2. How do Newton's Laws apply to objects and pulleys?

Newton's Laws apply to objects and pulleys in the same way as they apply to any other objects in motion. The first law states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. The second law states that the force applied to an object is equal to its mass multiplied by its acceleration. The third law states that for every action, there is an equal and opposite reaction.

3. How does a pulley affect the motion of an object?

A pulley can change the direction of the force applied to an object and can also multiply the force. For example, a single fixed pulley can change the direction of the force, while a system of multiple pulleys can multiply the force applied to an object.

4. What is the difference between a fixed pulley and a movable pulley?

A fixed pulley is attached to a stationary object and only changes the direction of the force applied. A movable pulley is attached to the object being moved and changes both the direction and the magnitude of the force applied.

5. How can Newton's Laws be used to solve problems involving objects and pulleys?

To solve problems involving objects and pulleys, you can use Newton's Laws and apply them to the system of objects. This involves identifying all the forces acting on the objects, using the equations for Newton's Laws, and solving for the unknown quantities. It is also important to draw free body diagrams to visualize the forces acting on the objects.

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