The mass of the block m the figure below is m and the angle theta. Find a model

Question

The mass of the block m the figure below is m and the angle theta. Find a model for the tension in the rope. If the cord is cut, find a model for the magnitude of the resulting acceleration of the block. Find the tension if the theta = 30 degree and the mass, m = 10 kg. Find the magnitude of the resulting acceleration of the block for the angle and mass in part C. Find the Tension if the mass is doubled. Find the acceleration if the mass is doubled. What angle would be needed to double the acceleration found m part D.

Explanation / Answer

A)as the block is at rest,
tension is balancing the component of the weight of the block along the incline.

hence tension T=m*g*sin(theta)

B)

if the cord is cut, then the block is free to slide down along the incline as there is no friction force to oppose the motion.

hence acceleration=component of acceleration due to gravity along the incline
=g*sin(theta)

C)theta=30 degrees

m=10 kg

then tension=m*g*sin(theta)=49 N

D)acceleration=g*sin(theta)=4.9 m/s^2

E)as tension is directly proportional to mass, if mass is doubled, tension is also doubled.

hence tension=2*49=98 N

F)as acceleration does not depend upon mass, there will be no change in acceleretion

hence acceleration=4.9 m/s^2

G)a=g*sin(theta)

let acceleration doubles at angle theta1.
then 2*a=g*sin(theta1)

==>2*4.9=9.8*sin(theta1)

==>sin(theta1)=1

==>theta1=90 degrees

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