A pendulum consisting of a string of length L=1.85 m attached to a bob of mass m=4.13 kg swings in a vertical plane. When the string is at an angle 16.0 degrees to the vertical, what is the tangential component of acceleration of the bob?
thanks for your help!
thanks for your help!
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You need to first find the tangential FORCE, because then you can use the equation:
tangential_acceleration = tangential_force / m
(that's just the same equation as "F=ma")
To find the tangential force, look at all the forces acting on the bob, and add up the tangential components of the individual forces.
The only forces are: the tension of the string, and bob's weight.
The tension has NO tangential component, because it pulls in a direction perpendicular to the tangential direction.
The weight has a tangential component equal to: (mg)sin(16°) (draw a diagram to convince yourself of that).
So, the total tangential force is: (mg)sin(16°)
And therefore the tangential component of the acceleration is:
(mg)sin(16°) / m
or:
(g)sin(16°)
Note that the bob's mass and the length of the string are irrelevant to this question.
tangential_acceleration = tangential_force / m
(that's just the same equation as "F=ma")
To find the tangential force, look at all the forces acting on the bob, and add up the tangential components of the individual forces.
The only forces are: the tension of the string, and bob's weight.
The tension has NO tangential component, because it pulls in a direction perpendicular to the tangential direction.
The weight has a tangential component equal to: (mg)sin(16°) (draw a diagram to convince yourself of that).
So, the total tangential force is: (mg)sin(16°)
And therefore the tangential component of the acceleration is:
(mg)sin(16°) / m
or:
(g)sin(16°)
Note that the bob's mass and the length of the string are irrelevant to this question.