A simple pendulum is oscillating with an angular amplitude 60°.If mass of bob is 50 gram the tension in the string at mean position is(g=10m/s2)
max ke = max Pe = m g h
h = r (1-cos 60) = r/2
so max (1/2) m v^2 = m g r/2
max v^2 = g r
T = m g + m v^2/r
T = m (g + g) = 2 m g = 2(.05)(10)
T = 1 Newton
Super
To find the tension in the string at the mean position of the simple pendulum, we can use the concept of gravitational force and equilibrium.
Given:
Angular amplitude (θ) = 60°
Mass of the bob (m) = 50 grams = 0.05 kg
Acceleration due to gravity (g) = 10 m/s^2
Step 1: Convert the angular amplitude from degrees to radians.
Since 1 radian = 180°/π, we have:
θ (in radians) = (60° × π) / 180°
= π/3 radians
Step 2: Calculate the gravitational force acting on the bob.
The gravitational force (F_g) is given by the formula:
F_g = m × g
Substituting the values, we get:
F_g = 0.05 kg × 10 m/s^2
= 0.5 N
Step 3: Determine the tension in the string at the mean position.
At the mean position, the tension in the string (T) is equal to the gravitational force acting on the bob.
Therefore, T = F_g = 0.5 N
So, the tension in the string at the mean position of the simple pendulum is 0.5 Newtons.
To find the tension in the string at the mean position of a simple pendulum, we can use the equation for gravitational force acting on the bob.
The equation is given by:
T = mg + mgcosθ
Where:
T is the tension in the string,
m is the mass of the bob,
g is the acceleration due to gravity, and
θ is the angular displacement from the vertical.
In this case, the angular amplitude is given as 60°. The mean position of a simple pendulum is when it is at the vertical position, which means θ = 0°.
Let's substitute the given values into the equation:
m = 50 grams = 0.050 kg (since 1 kg = 1000 grams)
g = 10 m/s^2
θ = 0°
T = (0.050 kg)(10 m/s^2) + (0.050 kg)(10 m/s^2)(cos(0°))
T = 0.5 N + 0.5 N
T = 1 N
So, the tension in the string at the mean position of the simple pendulum is 1 Newton.