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A bowling ball rolls without slipping up a ramp that slopes upward at an angle (beta) to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.
What is the acceleration of the center of mass of the ball?
Express your answer in terms of the variable (beta) and appropriate constants.(this was g*sin(beta)/1.4)
What minimum coefficient of static friction is needed to prevent slipping?
Express your answer in terms of the variable (beta) and appropriate constants.
The second part I don't understand how to do. Help is appreciated :/
A bowling ball rolls without slipping up a ramp that slopes upward at an angle (beta) to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.
What is the acceleration of the center of mass of the ball?
Express your answer in terms of the variable (beta) and appropriate constants.(this was g*sin(beta)/1.4)
What minimum coefficient of static friction is needed to prevent slipping?
Express your answer in terms of the variable (beta) and appropriate constants.
The second part I don't understand how to do. Help is appreciated :/

Respuesta :

MissPhiladelphia
To prevent slipping, the frictional force mus be less than the maximum static friction force. We'll assign constants like α to designate the ratio of the opposite and adjacent sides of the ramp. Then, the frictional force is equal to αma. It was determined previously that a=g*sin(beta)/1.4. So the frictional force becomes αmgsinβ. Meanwhile, the maximum static friction force or the normal force is kmgcosβ, where k is the minimum coefficient of static friction.

Equating both terms:

αmgsinβ = kmgcosβ

k = α (sinβ/cosβ)

From trigo functions, sinβ/cosβ is equivalent to tanβ

Thus, the minimum coefficient of static friction is k= αtanβ.

Friction is an opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N) . The minimum coefficient of static friction is k= αtanβ.

What is the friction force?

It is a type of opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N). Mathematically it is defined as the product of the coefficient of friction and normal reaction.

On resolving the given force and accelertaion in the different components and balancing the equation gets.Components in the x-direction

To find acceleration on an inclined plane

Masina-F= ma

mgcosa=R

F=μR

The frictional force must be smaller than the maximal static friction force to prevent slippage. To denote the ratio of the opposite and adjacent sides of the ramp, we'll use constants like.

The frictional force is equal to ma at this point. Previously, it was discovered that a=gsinβ

As a result, the frictional force is mgsinβ. Meanwhile, kmgcosβ is the maximum static friction force or normal force, where k is the minimum static friction coefficient.

Equating both terms:

[tex]\alpha mg sin\beta= kmgcos\beta\\\\ \rm k = \alpha (sin\beta /cos\beta)[/tex]

[tex]\rm \frac{SIN\beta}{cos\beta} = tan\beta[/tex]

[tex]\rm k = \alpha tan\beta[/tex]

Thus, the minimum coefficient of static friction is k= αtanβ.

To know more about friction force refer to the link;

https://brainly.com/question/1714663