Worksheet
Practice: Vertical Circular Motion
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Refer to the following information for the next four questions.
A 250-gram pendulum bob is initially constrained at a 53º angle by two strings as shown below.
What is the initial tension in the diagonal string?
What is the initial tension in the horizontal string?
When the horizontal string is cut the pendulum begins to swing. As the pendulum bob passes through its equilibrium position, what will be its velocity?
As the pendulum bob passes through its equilibrium position, what will be the tension in the supporting string?
Refer to the following information for the next six questions.
A ball of mass
m
is being whirled counterclockwise in the vertical circle of radius
r
as shown below.
Which expression below correctly describes the magnitude of the critical velocity needed by the bob in order to pass through point C and not leave its circular path?
What would be the tension in the string at point C if the ball were to be traveling at twice its minimal, critical velocity?
T = mg
T = 2 mg
T = 3 mg
T = 4 mg
T = 5 mg
If the following vector represents the weight of the ball,
then which vector could correctly represent the tension in the string as the ball passes through point A?
How fast would the ball be traveling if the tension at point A were three times its weight?
Suppose after several revolutions, the string suddenly breaks while the bob is passing through point B. Which of the following statements correctly describes the bob's motion after the strong breaks?
the mass follows a parabolic trajectory taking it upwards and to the left
the mass rises vertically straight up and then falls back towards the ground along the same vertical path
the mass follows a parabolic trajectory taking it upwards and to the right
the mass immediately falls straight downward
Suppose instead, that after several revolutions the string suddenly breaks while the bob is passing through point D. Which of the following statements correctly describes the bob's motion after the strong breaks?
the mass follows a parabolic trajectory taking it upwards and to the left
the mass rises vertically straight up and then falls back towards the ground along the same vertical path
the mass follows a parabolic trajectory taking it upwards and to the right
the mass immediately falls straight downward
Refer to the following information for the next three questions.
A 1-kg block is released from rest on a incline of height H. At the base of the ramp it encounters a loop-the-loop track having a radius of 80 cm.
What is the value of H if the block just barely remains in contact with track at the top of the loop-the-loop?
What is the normal force that the track exerts on the block as the block passes through the bottom of the loop-the-loop?
After passing through the loop-the-loop, the block slides off the track 80 cm above the ground while the track is at an angle of 37º. How far is the block's impact point with the ground from its last point of contact with the track?
Refer to the following information for the next question.
A 250-g block of wood is at rest at the bottom of a loop-the-loop section of track when it is struck by a 5-g bullet initially moving at speed v
_{o}
. Upon impact the bullet becomes embedded in the wood.
How fast was the bullet traveling prior to striking the block if the bullet/block combination just slides through the top of the loop-the-loop without losing contact with the track?
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