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ll_lordomega
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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.
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?
Fnet = ma (mass is in kg) ; v(final)^2 = v(initial)^2 + 2a(change in x)
kinetic friction = uk Fn ;
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.
Summary: I'm going crazy, please help.
EDIT: Why does that template copy when you preview? Whatever.
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.
Summary: I'm going crazy, please help.
EDIT: Why does that template copy when you preview? Whatever.
