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A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plump bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is
- a)Zero
- b)30º
- c)45º
- d)60º
Correct answer is option 'C'. Can you explain this answer?
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The angle made by the rod with the track is 30 degrees.
To determine this, we can consider the forces acting on the plumb bob.
Since the car is moving in a circular path, there must be a centripetal force acting towards the center of the circle to keep the car moving in a curved path. This force is provided by the tension in the rod.
The weight of the plumb bob acts downward and can be resolved into two components: one parallel to the track and one perpendicular to the track. The component parallel to the track does not affect the tension in the rod, as it is balanced by the normal force from the track.
The component perpendicular to the track is balanced by the tension in the rod. This creates a right triangle with the rod as the hypotenuse, the perpendicular component as the adjacent side, and the radius of the track as the opposite side.
We can use the trigonometric relationship cosine to solve for the angle made by the rod with the track.
cos(angle) = adjacent/hypotenuse
cos(angle) = radius/length of the rod
cos(angle) = 10/1
angle = arccos(10/1)
angle ≈ 30 degrees
Therefore, the angle made by the rod with the track is approximately 30 degrees.
To determine this, we can consider the forces acting on the plumb bob.
Since the car is moving in a circular path, there must be a centripetal force acting towards the center of the circle to keep the car moving in a curved path. This force is provided by the tension in the rod.
The weight of the plumb bob acts downward and can be resolved into two components: one parallel to the track and one perpendicular to the track. The component parallel to the track does not affect the tension in the rod, as it is balanced by the normal force from the track.
The component perpendicular to the track is balanced by the tension in the rod. This creates a right triangle with the rod as the hypotenuse, the perpendicular component as the adjacent side, and the radius of the track as the opposite side.
We can use the trigonometric relationship cosine to solve for the angle made by the rod with the track.
cos(angle) = adjacent/hypotenuse
cos(angle) = radius/length of the rod
cos(angle) = 10/1
angle = arccos(10/1)
angle ≈ 30 degrees
Therefore, the angle made by the rod with the track is approximately 30 degrees.
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A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plump bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track isa)Zerob)30ºc)45ºd)60ºCorrect answer is option 'C'. Can you explain this answer?
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