A 0.60 kg mass is attached to a 0.6 m string and displaced at an angle of 15 degrees before it is released. 1)What is the potential energy of the pendulum? 2) What is the angular frequency of the pendulum? What is the height of its displacement? 4) What is the velocity of the pendulum at the lowest point in its swing?
a man pushes a lawn mower 50 feet in 5 second by exerting a force of 30 pounds at an angle of 53
a man pushes a lawn mower 50 feet in 5 second by exerting a force of 30 pounds at an angle of 53 with the horizon. find the work done and the average power expended?
P.E=mgh=,m=0.60kg,g=0.6g,h=15ms-1square 0.60*0.6*15=?
To answer the given questions, we'll need to use the formulas and concepts related to potential energy, angular frequency, displacement, and velocity of a pendulum. Let's find the answers step by step:
1) Potential Energy of the Pendulum:
The potential energy of a pendulum depends on its displacement from the equilibrium position. The formula for potential energy is given by:
Potential Energy (PE) = m * g * h
Where:
m = mass of the object attached to the string (0.60 kg)
g = acceleration due to gravity (9.8 m/s²)
h = height of the displacement (since the pendulum is initially at an angle, h is the vertical height difference between the lowest point in the swing and the equilibrium position)
To find h, we can use the following equation:
h = L * (1 - cosθ)
Where:
L = length of the string (0.6 m)
θ = displacement angle (15 degrees)
First, convert the angle from degrees to radians:
θ (in radians) = θ (in degrees) * π / 180
Substituting the given values:
θ (in radians) = 15 * π / 180 ≈ 0.2618 radians
Now, calculate h:
h = 0.6 * (1 - cos(0.2618))
2) Angular Frequency:
The angular frequency (ω) of a pendulum is related to its length and gravitational acceleration. The formula for angular frequency is given by:
Angular Frequency (ω) = √(g / L)
Using the given values:
ω = √(9.8 / 0.6)
3) Height of Displacement:
We've already calculated the height (h) in the first step. h = 0.6 * (1 - cos(0.2618))
4) Velocity at the Lowest Point:
The velocity at the lowest point in a pendulum's swing is dependent on the conservation of mechanical energy. The formula for velocity (v) is given by:
Velocity (v) = √(2 * g * h)
Substituting the calculated value of h:
v = √(2 * 9.8 * h)
Now, let's substitute the calculated values into the respective formulas to find the answers.
Please note that the given values are assumed to be accurate for the purpose of calculation.