This problem is driving me crazy. It involves an incline, two masses and a rope.

• ll_lordomega
In summary, the conversation discusses a problem where a block is attached to a second block that is hanging freely by a string over an inclined plane. The problem involves finding the speed of the second block after it has fallen a certain distance. The solution involves using Newton's second law and applying it to the whole system of the two blocks and the rope. The conversation ends with the person asking for help as they are getting different results than what is in the book.
ll_lordomega
This has been driving me crazy because I thought I knew what I was doing, but the book says I'm wrong. I even worked backwards the answer in the book and it makes no sense to me. Please work this out and tell me what I'm doing wrong.

Homework Statement

A block of mass m1 = 250g is at rest on a plane that makes an angle of theta = 30 with the horizontal. The coefficient of kinetic friction between the block and the plane is 0.100. The block is attached to a second block of mass m2 = 200g that hangs freely by a string that passes over a frictionless, massless, pulley. When the second block has fallen 30.0 cm, what will its speed be?

Homework Equations

Fnet = ma (mass is in kg) ; v(final)^2 = v(initial)^2 + 2a(change in x)

kinetic friction = uk Fn ;

The Attempt at a Solution

I started by drawing the first block. I changed the axes so that the surface of the incline would be the x-axis and the y-axis would be the direction of the normal force. So, the forces here should be kinetic friction, tension, normal force, and gravity. I then split gravity (which is .25 * 9.8, or 2.45 N) into its x and y components. Since the incline is 30 degrees, the force of gravity makes a 60 degree angle with its x component. Thus, the x value is 2.45cos(60). And the y value, 2.45sin(60). Thus, the normal force is 2.45sin(60), or 2.12N. I then calculated the magnitude of kinetic friction, which is .212N. I will also mention at this point that the x value of gravity was 1.23 N. Next, I got the force of gravity for the second block, 1.96 N. I think this is the magnitude of the tension of the first block. I then used Newtons second law to get a = 2.07 m/s^2. But I think I must misunderstand tension, because I added the friction force and x value of the gravity force for the first block to get what the tension force on the other block should be. I then used Newtons law again for the second block and got a different acceleration. Either way, I get a different velocity than the one it says in the book. And yes, I used all kilograms and meters.

EDIT: Why does that template copy when you preview? Whatever.

The mg of the 2nd block is not the tension force. See this by applying
sum of forces = ma to the 2nd block.
mg - T = ma, so T = mg - ma. NOT just mg.

The two blocks and the rope are one system with the same acceleration. Apply
sum of forces = ma
to the whole works. Take that mg as positive, the component of force down the ramp and the friction as negative because they oppose the motion. Use the combined mass in the ma part.

Once you know the acceleration, just use accelerated motion formulas to find the speed.

Thanks a lot.

1. What is the purpose of the incline, two masses, and rope in this problem?

The purpose of these elements is to study the principles of mechanics, specifically the relationship between forces, mass, and motion. The incline represents an inclined plane or slope, while the masses and rope represent objects and the force acting upon them.

2. How do the masses and the incline affect the movement of the objects?

The masses and incline play key roles in determining the acceleration and direction of the objects. The incline provides a component of the force of gravity, while the masses experience a tension force from the rope. The angle of the incline and the masses' masses also affect the acceleration of the objects.

3. How can I calculate the forces and acceleration in this problem?

To calculate the forces, you can use the equations F=ma and F=mg*sin(theta), where F is force, m is mass, a is acceleration, g is the gravitational constant, and theta is the angle of the incline. The acceleration can be found using the equation a=(F-Ffr)/m, where Ffr is the force of friction.

4. What is the significance of this problem in the field of mechanics?

This type of problem is commonly used in the study of mechanics to understand the relationship between forces, mass, and motion. It also allows for the application of various equations and principles, such as Newton's Laws of Motion and the concept of work and energy.

5. How can I use this problem to apply my knowledge to real-world situations?

Understanding the principles and calculations involved in this problem can be applied to many real-world scenarios, such as calculating the force and acceleration of a car going up a hill, or determining the tension on a rope in a pulley system. This problem serves as a practical example of how mechanics can be used to analyze and solve real-world problems.

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