A conical pendulum rotates at 100 rev/min. The cord is 150mm long and the mass of the bob is 1.35kg. Find (a)the amount by which the bob rises above its lowest position , (b)the periodic time , (c)the tension in the cord . ( PLEASE HELP ME FOR MY REPORT )
Sure! Let's break down your question into three parts and find the answers step by step.
(a) The amount by which the bob rises above its lowest position:
To find the amount by which the bob rises above its lowest position, we need to consider the forces acting on the system. In this case, we have two forces acting: the tension in the cord (T) and the weight of the bob (mg).
The weight of the bob can be calculated using the formula: weight = mass × gravitational acceleration (w = mg). In this case, the mass of the bob is given as 1.35kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
So, the weight (w) of the bob is:
w = 1.35kg × 9.8 m/s^2
Next, let's look at the forces acting on the bob when it swings in a circular motion. At the lowest point of the swing, the tension in the cord is equal to the weight of the bob (T = w). At the highest point, the net force is equal to the difference between the tension and weight (T - w).
Using this information, we can calculate the amount by which the bob rises above its lowest position as follows:
Let h be the height by which the bob rises above its lowest position.
So at the highest point, the net force is T - w = mv^2 / r, where v is the velocity and r is the length of the cord.
Since the bob is moving in a circular path, its linear velocity (v) can be calculated as:
v = ωr,
where ω is the angular velocity given in revolutions per minute (rpm). To convert it to radians per second (rad/s), we need to multiply ω by 2π / 60.
Substituting the values into the equation, we have:
T - w = mv^2 / r
T - w = m(ω^2)r^2 / r
T - w = mω^2r
T - w = m(2πω / 60)^2r
At the lowest point, the tension in the cord is equal to the weight (T = w), so we have:
w - w = m(2πω / 60)^2r
0 = m(2πω / 60)^2r
0 = m(2π(100) / 60)^2(0.15)
Solving for h, we get:
h = 0.5 × m(2π(100) / 60)^2(0.15)
Now, substitute the given values for mass (m), angular velocity (ω), and length (r) into the equation to find the answer.
(b) The periodic time:
The periodic time is the time taken for one complete revolution or swing of the bob. It can be calculated using the formula: T = 1 / f, where f is the frequency.
In this case, the frequency is given as 100 revolutions per minute (rev/min). To convert it into hertz (Hz), we divide by 60.
So, the periodic time (T) is:
T = 1 / (100 / 60)
Simplifying the equation will give you the answer.
(c) The tension in the cord:
At the lowest point, the tension in the cord is equal to the weight of the bob (T = w). So, we can use the weight (w) calculated in part (a) to find the tension.
Substitute the weight (w) into the equation to find the tension.
Now you have the step-by-step instructions to find the answers to your questions. Good luck with your report!