Finding Acceleration in a Frictionless System with Multiple Masses

In summary, the conversation discusses how to calculate the acceleration of three masses (m1 = 0.9kg, m2 = 1.6kg, and m3 = 2.4kg) on a frictionless table. The suggested method is to draw free body diagrams and use Newton's second law to solve for the acceleration and tension in the system. The tension is the same throughout the entire system and the forces in the y direction cancel out, leaving only the forces in the x direction to consider.
  • #1
jessicax07
7
0

Homework Statement



What is the acceleration of the masses as shown in the second attached image. m1 = 0.9kg, m2 = 1.6kg, and m3 = 2.4kg. (Assume the table is frictionless)

Homework Equations



[tex]\sum[/tex]F=ma
F_mg+FN = ma

The Attempt at a Solution



I figured everything up to the point a=F/(m1+m2+m3) but without the force given, how do you figure it out?
 

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  • #2
Draw free body diagrams. Isolate the hanging block...what are the forces acting on it? Then use Newton 2 on that blck to arrive at an equation. Then isolate the 2 blocks together on the table, determine the forces acting on that free body diagram of those 2 blocks, and apply Newton 2 to that system to get another equation. Now you solve 2 equations with 2 unknowns to find he aceleration. Note that the magnitude of the acceleration of each block must be the same.. Note also that the magnitude of the tension in a cord wrapped around an ideal pulley is the same on both sides of the pulley.
 
  • #3
Even by doing that though, I don't see how I'd find a because like you said there would be 2 unknowns...
 
  • #4
jessicax07 said:
Even by doing that though, I don't see how I'd find a because like you said there would be 2 unknowns...
Yes, the 2 unknowns are the cable tension, T, and the acceleration, a. Solve the 2 simultaneous equations by the method of your choice.
 
  • #5
Tension is uniform through out the entire net system. Knowing that, isolate each system (isolate each block), sum the forces in each system and then use substitution to find a. Obviously the forces in the y direction cancel the first two block is zero so you only need to work about Fx. The forces in the x direction for the third block are zero, so you only need to worry about the y direction
 

Related to Finding Acceleration in a Frictionless System with Multiple Masses

What are Newton's Laws of Motion?

Newton's Laws of Motion are three fundamental principles of physics that describe the relationship between an object's motion and the forces acting upon it. They were developed by Sir Isaac Newton in the late 17th century and are still used today to explain and predict the behavior of objects in motion.

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 at a constant velocity unless acted upon by an unbalanced force. In other words, an object will not change its state of motion unless a force is applied to it.

What is the Second Law of Motion?

The Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be. However, the more mass an object has, the harder it is to accelerate.

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 an object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

How are Newton's Laws of Motion used in everyday life?

Newton's Laws of Motion are used in many everyday activities, such as driving a car, riding a bike, or even walking. They also play a crucial role in the design and functioning of machines and structures, from simple tools to complex vehicles. Understanding these laws can help us make predictions and solve problems related to motion and force.

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