Download In each of the following situations:-

Forces in Circular Motion
In each of the following situations: draw the forces acting on the object,
 draw the acceleration vector
 write the expression for Newton’s 2nd law involving the identified forces.
The experience of weightlessness occurs when the reaction force for the surface is zero. Indicate
whether “weightlessness’ is possible in the situation, and if so what is the relationship between the
radius and velocity?
Car travelling over a crest in a road
Car travelling through a dip in the road
Roller coaster at bottom of loop
Roller coaster at top of loop
Car turning left
Car on a banked road
Bike turning left
Astronaut in plane experiencing “weightlessness”
Water in a swinging bucket
Explain how the water can stay in the bucket as you swing your arm around.
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Estimate the slowest speed the bucket can have at the top for the water to stay in the bucket
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Forces in Circular Motion - Answers
Car travelling over a crest in a road
N
Car travelling through a dip in the road
N
a
a
mg
N – mg = ma = mv2/r
mg
mg – N = ma = mv2/r
Weightlessness is possible, when N = 0,
mg = mv2/r,
v2 = gr
Roller coaster at bottom of loop
N
a
Roller coaster at top of loop
N
A
Mg
N – mg = ma = mv2/r
N
mg
mg + N = mv2/r
Restraining rail keeps
faster trolley on rails by
providing a downwards
reaction force
Car on a banked road
mg
mg – N = ma = mv2/r
Weightlessness is possible,
When N=0, mg = mv2/r,
v2 = gr
Car turning left
T

mg
Friction
a
Friction = ma = mv2/r
Bike turning left
N
Friction
mg
a
Tcos = mg
Tsin = ma = mv2/r
N
Mg
N
a
mg

Nsin = ma = mv2/r, Ncos = mg
Astronaut in plane experiencing “weightlessness”
N

mg
Friction = mv2/r or Ncos = mv2/r
Water in a swinging bucket
At Top
a
mg
mg = ma = mv2/r
Weightlessness, when v2 = gr
At Bottom
N
a
a
mg N
mg
mg + N = mv2/r
N – mg = mv2/r
Explain how the water can stay in the bucket as you swing your arm around.
At the top the acceleration is down because the weight and reaction force are down, but the water is
travelling horizontally. The change in vel is down, so the new velocity is angled down along the tangent
to the circle.
Estimate the slowest speed the bucket can have at the top for the water to stay in the bucket
N = 0. Assume a shoulder to bucket distance of 100cm, then v2 = gr = 10 x 1.00, so v = 3.2 m/s.
Extension: Find the Period and theTension in the arm at bottom, assuming constant speed.