Vertical Circles

Question 1

What properties does an object moving in a vertical circle have?

Answer 1

An object moving in a vertical circle has a changing height above the ground.
Constant angular displacement and angular velocity
Constant time period and frequency
Constant magnitude of centripetal acceleration and force

Question 2

What a two features of a ball being swung on the end of a string?

Answer 2

1) The tension will always act along the string, towards the centre of the circle
2) The weight will always act down towards Earth

Question 3

Calculate the size of the centripetal force required to move an object of mass 230 g in a circle of radius 80.0 cm at an angular velocity of 8.50 rad s-1

Calculate the weight of the object

Answer 3

1. F = mrω^2 = 13.294 = 13.3 N

2. W = mg = 2.2563 = 2.3 N

Question 4

What happens when the ball on string is at the bottom of the vertical circle?

Answer 4

At the bottom of a vertical circle:
Weight acts away from the centre (2.3 N down)
Tension must provide the normal reaction force to the weight (2.3 N up) and the centripetal force towards the centre (13.3 N up)
Tension must be 15.6 N

Question 5

What happens when the ball on string is at the top of the vertical circle?

Answer 5

Weight acts towards the centre (2.3 N down)
Tension only needs to provide the additional force required for the centripetal force towards the centre (13.3 N down)
Tension must be 11.0 N

Question 6

What happens when the ball on string is level with the centre of the circle?

Answer 6

Weight has no component in the direction of the centre (0 N)
Tension must provide the centripetal force towards the centre (13.3 N horizontally)
Tension must be 13.3 N

Question 7

How can you find centripetal force with weight and tension anywhere on the circle

Answer 7

Centripetal force
=
weight (vector component acting towards the centre)
\+
tension

Question 8

Describe and explain how the tension in string of an object being spun in a vertical circle varies at different points in the circle.

Answer 8

Describe:

tension is at a maximum at the lowest point
tension is at a minimum at the highest point
tension varies (sinusoidally) between these points
tension is greater than mv2/r in the bottom half of the circle
tension is less than mv2/r in the top half of the circle

Explain:

a centripetal force of mv2/r must always be provided to keep the object moving in a circle
at the highest point a portion of this force is provided by mg, so tension is lower.
at the lowest point the tension must provide the centripetal force and act against mg, so tension is higher
at other points the tension varies depending on the component of mg acting towards the centre

Question 9

What do questions with an object on a string look like?

Answer 9

The object is physically attached the the centre of the circle
The object is undergoing circular motion because the string is attached to it
Generally, you are considering tension in the string and weight

Question 10

What do questions with an object on the inside surface of a loop/circle look like?

Answer 10

Examples: sock in a washing machine, roller coaster car inside a loop
The object is not physically attached to the centre of the circle
The object is undergoing circular motion because a solid object is providing a force inwards
Generally, you are considering contact force and weight

Question 11

What do questions with an object on the outside surface of a loop/circle look like?

Answer 11

Example: car going over a bridge
The object is not physically attached to the centre of the circle
The object is undergoing circular motion because its weight can provide the centripetal force
Generally, you are considering weight and the reaction contact force from the ground

Question 12

A roller coaster has a vertical loop of radius 12m. The cars travel round the loop at 14ms^-1. Calculate:

a) the centripetal force needed for a passenger of mass 60kg
b) the contact forces on the passenger at the top and bottom of the loop
c) the point where the passenger feels heaviest

Answer 12

a) Centripetal force = mv2/r = (60 x 142)/ 12 = 980 N

b) Passenger weight = mg = 60 x 9.8 = 590 N
At the top of the loop:
980 N must act towards the centre
weight acts towards the centre, providing 590 N
The contact force only needs to be (980 - 590) = 390 N
At the top of the loop:
980 N must act towards the centre
weight acts away from the centre, providing -590 N
The contact force needs to be (980 - (-590)) = 1570 N

c) The passenger feels ‘heaviest’ when the contact force acting on them is greatest. This is at the bottom of the loop

Question 13

What is the minimum speed for a roller coaster with a vertical loop of radius 12 m?

Answer 13

10.9 ms^-1