A ball attached to a 1.25 metres string is spun around with a period of 0.25 seconds calculate:
a)its average speed
b)its average velocity after completing 10 complete turns.
c)its average velocity after completing 5 1/2 ten turns.
could u please show all working out. I had a go at it but I couldn't figure it out
Thanks in advance
a)its average speed
b)its average velocity after completing 10 complete turns.
c)its average velocity after completing 5 1/2 ten turns.
could u please show all working out. I had a go at it but I couldn't figure it out
Thanks in advance
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Ok we will look at a couple different concepts here.
First, the difference between velocity and speed. Velocity is a magnitude (speed) times a direction giving us a vector. Also we know that speed does not depend on direction which will be the difference between a and the last two parts.
If we look at velocity vectorally in circular motion we know the magnitude of it will always be the tangential speed. However, the direction will constantly change. If you look at the velocity at any given point, it will have a counterpart on the other side of the circle with the same magnitude but the opposite direction. To see this for yourself, draw a circle and make a tangent line to show the direction of the velocity at any given point. Then go 180 degrees to the other side and you will see the velocity will be in the opposite direction. So from this we know in one revolution each velocity will have another velocity that cancels it out so the average velocity will be zero. We can also look at this in the fact that velocity is the change in position with respect to time. If we know this when the object returns to the starting point after one revolution it will have a 0 displacement. If displacement=0 velocity= 0
b.) 0
For part a we can look at it purely mathematically.
v (as in the magnitude of velocity or speed) = (2pi*r)/T (the period)
T=.25 seconds and r=.625 or half the length of the string
so we see its average speed is
v=(2*pi*.625)/0.25= 15.7 m/s
Now for c it goes back a little to the first concept, except it goes 5 1/2 turns. So we know the average velocity will not be equal to zero.
We will actually calculate the total displacement and divide by the total time here.
Displacement in this case will be equal to half the diameter or
(2pi*r)/2
=3.9 meters
Now we know it went around 5 1/2 times and it takes .25 seconds for each revolution so
t= 5.5T= 1.375 seconds
so the average velocity will be
3.9/1.375=
2.8 m/s opposite the direction of the origin.
First, the difference between velocity and speed. Velocity is a magnitude (speed) times a direction giving us a vector. Also we know that speed does not depend on direction which will be the difference between a and the last two parts.
If we look at velocity vectorally in circular motion we know the magnitude of it will always be the tangential speed. However, the direction will constantly change. If you look at the velocity at any given point, it will have a counterpart on the other side of the circle with the same magnitude but the opposite direction. To see this for yourself, draw a circle and make a tangent line to show the direction of the velocity at any given point. Then go 180 degrees to the other side and you will see the velocity will be in the opposite direction. So from this we know in one revolution each velocity will have another velocity that cancels it out so the average velocity will be zero. We can also look at this in the fact that velocity is the change in position with respect to time. If we know this when the object returns to the starting point after one revolution it will have a 0 displacement. If displacement=0 velocity= 0
b.) 0
For part a we can look at it purely mathematically.
v (as in the magnitude of velocity or speed) = (2pi*r)/T (the period)
T=.25 seconds and r=.625 or half the length of the string
so we see its average speed is
v=(2*pi*.625)/0.25= 15.7 m/s
Now for c it goes back a little to the first concept, except it goes 5 1/2 turns. So we know the average velocity will not be equal to zero.
We will actually calculate the total displacement and divide by the total time here.
Displacement in this case will be equal to half the diameter or
(2pi*r)/2
=3.9 meters
Now we know it went around 5 1/2 times and it takes .25 seconds for each revolution so
t= 5.5T= 1.375 seconds
so the average velocity will be
3.9/1.375=
2.8 m/s opposite the direction of the origin.
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radius, r = 1.25 meter
Period, T = 0.25 sec
circumference = pi*r = 1.25pi = 3.927 m
a.
average-speed = 3.927/0.25 = 15.71 m/sec >=======< ANSWER
b.
10-turns = 3.927*10 = 39.27 m,
time = 10*0.25 = 2.5 sec
average-speed = 39.27/2.5 = 15.71 m/sec >=======< ANSWER
c.
Here, Also,
average-speed = 15.71 m/sec >==============< ANSWER
Period, T = 0.25 sec
circumference = pi*r = 1.25pi = 3.927 m
a.
average-speed = 3.927/0.25 = 15.71 m/sec >=======< ANSWER
b.
10-turns = 3.927*10 = 39.27 m,
time = 10*0.25 = 2.5 sec
average-speed = 39.27/2.5 = 15.71 m/sec >=======< ANSWER
c.
Here, Also,
average-speed = 15.71 m/sec >==============< ANSWER