A student swings a 3.5g rubber stopper in a horizontal circle over her head.The length of the string is 0.6m.The stopper is observed to make 10 revolutions in 11.7seconds.What is the tangential velocity of the stopper at any time,t.
The tangential speed at any time is
V = 10*(2*pi*R)/11.7 s = 3.375 m/s
The mass of the stopper has nothing to to with it.
The direction of the tangential veloity is forward and perpendical to the string. It keeps changing.
To find the tangential velocity of the stopper at any time, we can use the formula:
tangential velocity = (2 * π * r) / T
Where:
- tangential velocity is the velocity of the object moving in a circular path tangent to that path at any point
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the circular path
- T is the time period it takes for one complete revolution
Given:
- The length of the string/radius (r) = 0.6 m
- The number of revolutions (N) = 10
- The total time taken (t) = 11.7 s
First, calculate the time period (T) for one complete revolution:
T = t / N
T = 11.7 s / 10
T = 1.17 s/rev
Now, substitute the values in the formula:
tangential velocity = (2 * π * r) / T
tangential velocity = (2 * 3.14159 * 0.6) / 1.17
tangential velocity ≈ 3.214 m/s
Therefore, the tangential velocity of the stopper at any time is approximately 3.214 m/s.
To find the tangential velocity of the stopper at any time, we can use the formula:
v = 2πr / t
where:
- v is the tangential velocity (what we are looking for)
- π is a mathematical constant pi (approximately 3.14159)
- r is the radius of the circular path (length of the string in this case)
- t is the time taken to complete one revolution
In this problem, the length of the string is given as 0.6m. Since the stopper is swinging in a horizontal circle over the student's head, the radius of the circular path is equal to the length of the string.
We are also given that the stopper makes 10 revolutions in 11.7 seconds. This information is useful for determining the time taken for one revolution (t), as we can divide the total time by the number of revolutions.
t = 11.7 seconds / 10 revolutions
t = 1.17 seconds/revolution
Now we can substitute the values into the formula to calculate the tangential velocity (v):
v = 2πr / t
v = 2π(0.6m) / 1.17 seconds/revolution
When you plug in the numbers and calculate the expression, you will get the value of the tangential velocity in meters per second.