A conical pendulum consists of a 200g body at the end of a 40cm long string making 10degrees with the vertical
Find a) Velocity of the body
b) Tension in the string
tan 10 = m v^2/R / mg = v^2/(R g)
but R/0.40 = sin 10
so R = 0.40 sin 10
T = m sqrt [(v^2/R)^2 + g^2]
To find the velocity of the body in a conical pendulum and the tension in the string, we can use the principles of circular motion.
a) Velocity of the body:
In a conical pendulum, the motion is circular, so we can use the formula for the centripetal acceleration:
a = (v^2) / r
Where:
- a is the centripetal acceleration
- v is the velocity of the body
- r is the radius of the circular motion, which is the length of the string
Now, we can solve for v:
v = √(a * r)
To find the centripetal acceleration, we need to find the net force acting on the body. In this case, it is the component of gravitational force acting along the string.
Net Force = m * g * sin(θ)
Where:
- m is the mass of the body
- g is the acceleration due to gravity
- θ is the angle the string makes with the vertical
Now, we can solve for the centripetal acceleration:
a = (m * g * sin(θ)) / m
Substituting the given values:
- m = 200g = 0.2 kg (convert grams to kilograms)
- g = 9.81 m/s² (acceleration due to gravity)
- θ = 10 degrees (convert degrees to radians)
a = (0.2 kg * 9.81 m/s² * sin(10 degrees)) / 0.2 kg
Now, substitute this value of a and the given value of r (40 cm = 0.4 m) into the equation for v:
v = √(a * r)
Now, calculate the result.
b) Tension in the string:
The tension in the string is equal to the net force acting on the body. In this case, it is the vertical component of gravitational force.
Tension = m * g * cos(θ)
Where:
- m is the mass of the body
- g is the acceleration due to gravity
- θ is the angle the string makes with the vertical
Substituting the given values:
- m = 200g = 0.2 kg (convert grams to kilograms)
- g = 9.81 m/s² (acceleration due to gravity)
- θ = 10 degrees (convert degrees to radians)
Tension = 0.2 kg * 9.81 m/s² * cos(10 degrees)
Now, calculate the result.