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what is the acceleration ar(t) of the rod? take m to be the mass of the rod. express your answer as a function of v , b , the velocity of the rod vr(t) , l , r , and the mass of the rod m .

User Taudep
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Final Answer:

The acceleration ar(t) of the rod is expressed as ar(t) = (-b/m) * vr(t), where m represents the mass of the rod, vr(t) is the velocity of the rod, and b signifies a constant related to resistance or friction.

Step-by-step explanation:

The acceleration of the rod, ar(t), can be understood through Newton's second law, F = ma, where F denotes the net force acting on the rod, m is the mass, and a is the acceleration. Considering the resistance force proportional to the velocity of the rod, we apply the equation of motion for resistance, F = -bv. Rearranging to isolate acceleration, a = F/m = (-b/m) * v.

In this context, the resistance force opposing the motion of the rod is proportional to its velocity, represented by -bv, where 'b' is a constant related to the resisting medium (like air or friction) and 'v' is the velocity of the rod. By dividing this force by the mass 'm,' we derive the acceleration. Therefore, the acceleration ar(t) = (-b/m) * vr(t) shows that the rate of change of velocity of the rod is inversely proportional to its mass ('m') and directly proportional to the resisting factor 'b' and the velocity of the rod, vr(t).

This equation highlights that as the mass of the rod increases, the acceleration decreases, while an increase in the resistance constant 'b' or the velocity of the rod leads to a higher acceleration opposing its motion. It elucidates the dynamic relationship between mass, resistance, and velocity in determining the acceleration of the rod.

User TechCrap
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Final answer:

The acceleration of the rod, ar(t), can be determined by differentiating the velocity function, vr(t), with respect to time.

Step-by-step explanation:

The acceleration of the rod, ar(t), can be determined by differentiating the velocity function, vr(t), with respect to time. Since vr(t) is not provided in the question, we cannot directly calculate ar(t) using the given information. However, if we have the velocity function, we can differentiate it to find the acceleration function.

The function (3 * b * r2) / (m * l2) is used to calculate the rod's acceleration, with v denoting its velocity, b denoting its frictional force, vr(t) denoting its velocity, l denoting its length, r denoting its rotational radius, and m denoting its mass.

User TamarG
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