Applying Newton's Laws of Motion

In summary, two blocks, X and Y, with masses of 5.12kg and 3.22kg, respectively, are connected by a fishing line over a frictionless pulley. Block X slides up an incline at 35.7 degrees above the horizontal with a positive acceleration. The magnitude of the acceleration is 0.273m/s2. The solution involves calculating the net force, which is equal to the sum of the tension force and the gravitational force, and using the mass of both blocks. The tension force can be found by using the sine and cosine functions.
  • #1
emma3001
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Homework Statement



Blocks X and Y of masses mx=5.12kg and my=3.22kg are connected by a fishing line passing over a frictionless pulley. Show that block X slides up the incline (35.7 degrees above the horizontal) with positive acceleration. Determine the magnitude of the acceleration. (0.273m/s2 is the answer)


Homework Equations



Ftension-Fg=Fnet=m total x a system
sin35.7=Fty/Ftens
Cos35.7=Ftx/Ftens
Fg=mg (Block Y)

The Attempt at a Solution



I want to find the Ftx= and FAy but i do not know the Ftens. I can calculate the gravitational force of Block Y, which is F=mg=31.6N. now i am trying to figure out how to calculate the net force which will give me acceleration, using the combined mass of the two blocks. What is confusing me is the incline and the fact that no tension force is given.
 
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  • #2
please help me understand the situation at least! thx
 
  • #3


I would approach this problem by first identifying the relevant forces acting on the system. In this case, we have the force of gravity acting on both blocks, the normal force of the incline acting on block X, and the tension force in the fishing line connecting the two blocks.

Using Newton's Second Law, we can write the equation Fnet = ma, where Fnet is the net force acting on the system, m is the combined mass of the two blocks, and a is the acceleration of the system.

To determine the net force, we need to consider the forces acting on each block separately. For block X, we have the force of gravity pulling it down the incline and the normal force pushing it up the incline. The normal force can be calculated using the formula Fnormal = mgcosθ, where θ is the angle of the incline.

For block Y, we have the force of gravity pulling it down and the tension force pulling it up. Since the pulley is frictionless, the tension force will be equal to the weight of block X, which we can calculate using the formula Ftx = mgsinθ.

Now, we can write the equation for the net force as Fnet = (mX + mY)a, where mX and mY are the masses of blocks X and Y respectively.

Substituting in the forces we calculated for each block, we get:

Fnet = (mX + mY)a = (mXgcosθ - mYgsinθ) = (5.12kg)(9.8m/s²)(cos35.7°) - (3.22kg)(9.8m/s²)(sin35.7°) = 28.87N

Finally, we can solve for the acceleration by rearranging the equation to a = Fnet / (mX + mY) = 28.87N / (5.12kg + 3.22kg) = 0.273m/s².

Therefore, we can conclude that block X will slide up the incline with a positive acceleration of 0.273m/s².
 

FAQ: Applying Newton's Laws of Motion

What are Newton's Laws of Motion?

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

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 external force.

What is the second law of motion?

The second law of motion, also known as the Law of Force and Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be represented by the equation F=ma, where F is force, m is mass, and a is acceleration.

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 a force is exerted on an object, the object will exert an equal force in the opposite direction.

How can Newton's Laws of Motion be applied?

Newton's Laws of Motion can be applied in many real-world situations, such as calculating the forces acting on a moving car or predicting the trajectory of a projectile. They are also used in the design of machines and structures, as well as in the study of celestial bodies and their movements.

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