Newtons Laws - Boxes connected with a cord

In summary, the problem involves two blocks connected by a rope and a pulley, with block A resting on a tabletop and block B hanging. The coefficient of kinetic friction between block A and the tabletop is 0.45. The goal is to find the speed of each block after moving 3cm. The solution involves finding the friction force and the force on the rope, and then using Newton's second law and kinematics to solve for the tension and acceleration, and finally the speed of the blocks.
  • #1
hsestudent
8
0

Homework Statement


A block A (mass 2.25k) rests on a tabletop. It is connected by a horizontal cord passomg over a light, frictionless pulley to a hanging block B (mass 1.3kg). The coeffisient of kinetic friction between block A and the tabletop is 0.45. After the block is released from the rest,
fint the speed of each block after moving 3cm.


Homework Equations





The Attempt at a Solution


I found the frictionforce by:

Frictionforce = coeffisient * N (where N = G of block A).

Frictionforce = 9,93 N.

The force on the rope will be = the G (gravityforce) on block B.

ForceOnRope = 12,75N

Then I tried to use Newtons second law to find the acceleration, but this attempt failed when I tried to find the velocity of the boxes, which will be the same?
 
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  • #2
hsestudent said:
The force on the rope will be = the G (gravityforce) on block B.

ForceOnRope = 12,75N
The tension in the rope does not equal the weight of block B. If it did, then the blocks would be in equilibrium.

Call the tension T. Set up equations for both blocks and you'll be able to solve for the tension and the acceleration.
 
  • #3
tension

Note that the Tension will be the same throughout the rope. So if you set up the forces on each block and solve them for the Tension, you can then set those 2 equations equal to solve for other variables, such as the acceleration. Then you can use kinematics to solve for the speed.
 
Last edited:
  • #4
Thanks, will try this tomorrow morning!
 

Related to Newtons Laws - Boxes connected with a cord

1. What are Newton's Laws?

Newton's Laws are three fundamental principles of classical mechanics that describe the behavior of objects in motion. They were first published by Sir Isaac Newton in his book "Philosophiæ Naturalis Principia Mathematica" in 1687.

2. What is the First Law of Motion?

The First Law of Motion, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will remain in motion with a constant velocity, unless acted upon by an external force.

3. How does the Second Law of Motion apply to boxes connected with a cord?

The Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In the case of boxes connected with a cord, the acceleration of the boxes will depend on the force applied by the cord and the mass of the boxes.

4. What is the Third Law of Motion?

The Third Law of Motion, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. This means that when two objects interact, the force exerted by one object on the other is equal in magnitude and opposite in direction to the force exerted by the second object on the first.

5. How can Newton's Laws be applied in real-life situations?

Newton's Laws can be applied in various real-life situations, such as understanding the motion of objects in sports, designing vehicles and structures, and predicting the behavior of objects in space. They are also used in everyday activities, such as driving a car and throwing a ball.

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