Angular acceleration and tension

In summary, two blocks of mass 2.00 kg and 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk with a radius of 0.25 m and a mass of 10 kg. The blocks are allowed to move on a fixed block-wedge of angle 30 degrees, with a friction coefficient of 0.360 for both blocks. The goal is to find the acceleration of the blocks and the tensions in the string on both sides of the pulley. The equations for these values take into account the gravitational force, the coefficients of friction, and the angular acceleration of the pulley, which can be determined from its mass, size, and shape.
  • #1
Satoy
16
0
A block of mass 2.00 kg and a block of mass 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having a radius of .25 m and mass 10 kg. These blocks are allowed to move on a fixed block-wedge of angle 30 degrees. Friction = .360 for both blocks.

Ok I don't have a scanner but do you get the picture? The 2 kg block is sitting on a flat surface and the other is sitting on a 30 degree surface attached by a string that goes over a pulley at the change in slope point.

I basicly know the set up but having problems with making a equation. The first part is to find the acceleration of the blocks. This would be m_2*g*cos(30)-friction of M_1- friction of M_2. Is this right?

The second part is the tension of the strings on both sides of the pulley. All I can think of is T=m(g-a)

Please help need to understand finals next week.
 
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  • #2
Ok tension on M_1 has something to do with the pulley and T on m_2 should be greater but what is the equation? M_2 is the equation above but what is the other?
 
  • #3
You are forgetting the angular acceleration of the pulley. The pulley is not massless, so it has a moment of inertia which you can determine from its mass, size and shape.

The linear accelerations of the two blocks are equal, but the tensions in the string on each side of the pulley are not equal, so you can make two equations for the accelerations of the two blocks, and one for the angular acceleration of the pulley.
 

FAQ: Angular acceleration and tension

What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is a measure of how quickly an object's rotational speed is changing.

How is angular acceleration related to linear acceleration?

Angular acceleration and linear acceleration are related through the radius of rotation. The formula for linear acceleration is a = r * α, where a is linear acceleration, r is the radius, and α is angular acceleration.

What factors affect angular acceleration?

Angular acceleration is affected by the net torque applied to an object, the moment of inertia (which is dependent on an object's mass and distribution of mass), and the distance from the axis of rotation at which the force is applied.

What is tension in relation to angular acceleration?

Tension is the force exerted by a string or other material when it is pulled taut. In the context of angular acceleration, tension can be a source of torque which can affect an object's rotational motion.

How is tension calculated in a rotating system?

In a rotating system, tension can be calculated using the formula T = m * (v^2/r), where T is tension, m is the mass of the object, v is the linear velocity, and r is the radius of rotation. This formula takes into account the centripetal force required to maintain circular motion.

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