What is the tension force acting on the block?

In summary, a spherical shell of mass Ms and radius R rotates about a vertical axis with a light cord attached to a small block of mass m. The block is free to fall under gravity and is connected to a disk of mass Mp and radius r. The acceleration of the block can be found using the equation Fnet=ma, and the tension force acting on the block and sphere can be calculated using the equations Isphere=(2/5)Ms R^2 and Idisk=.5Mpr^2, and Torque =rxf=Is(angular a). A F.B.D. should be drawn to visualize the forces at play.
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1. A uniform sperical shell of mass Ms and radius R rotates about a vertical axis on frictionless bearings. A light cord passes around the equator of the shell over a pulley (a disk of mass Mp and radius r) and is attached to a small block of mass m that is otherwise free to fall under the influence of gravity.
A. What is the acceleration of the block?
B. What is the tension force acting on the block?
C. What is the tension force acting on the sphere?




Homework Equations


Isphere=(2/5) Ms R^2 Idisk=.5Mpr^2


3. Torque =rxf=Is(angular a)
RF=Is(angular a)
F=(2/5)MsR(ang. a)
Fnet=ma
Fs-mg=ma

 
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Draw an F.B.D..
 
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A. The acceleration of the block can be found by using the equation Fnet=ma, where Fnet is the net force acting on the block and m is its mass. We can also use the equation Fs-mg=ma, where Fs is the tension force and mg is the force of gravity acting on the block. Since the block is otherwise free to fall, we can assume that the acceleration due to gravity (g) is acting on it. Therefore, the acceleration of the block can be expressed as a = (Fs-mg)/m.

B. The tension force acting on the block can be found by using the equation Fs-mg=ma. We know that the mass of the block is m and the acceleration is a, so we can rearrange the equation to solve for Fs. Therefore, the tension force acting on the block is Fs = m(a+g).

C. The tension force acting on the sphere can be found by using the equation F=(2/5)MsR(ang. a), where F is the net force acting on the sphere and ang. a is the angular acceleration. Since the sphere is rotating at a constant speed, the angular acceleration is 0. Therefore, the tension force acting on the sphere is F = 0. This makes sense because the only forces acting on the sphere are the normal force from the bearings and the tension force from the cord passing over the pulley, which cancel each other out.
 

FAQ: What is the tension force acting on the block?

What is tension force?

Tension force is a type of force that is exerted when an object is pulled or stretched. It is a result of the interaction between two objects, where one object exerts a force on the other in the opposite direction.

How is tension force different from other types of forces?

Tension force is different from other types of forces because it is a result of pulling or stretching, while other forces such as gravity and friction are a result of pushing or resistance.

What factors affect the magnitude of tension force?

The magnitude of tension force is affected by the weight of the object, the angle of the rope or string, and the strength of the material used to create the rope or string.

How is tension force measured?

Tension force is measured in units of newtons (N) using a spring scale or a force meter. The scale or meter will show the amount of force being exerted on the object.

How can tension force be calculated?

Tension force can be calculated using the equation F = m*a, where F is the tension force, m is the mass of the object, and a is the acceleration of the object. It can also be calculated using the equation F = k*x, where k is the spring constant and x is the displacement of the spring or string.

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