A pendulum swings back and forth up to a maximum height of 1.52 m. Neglecting friction, what is the speed of the pendulum at the lowest position.
a) 2.7 m/s
b) 3.9 m/s
c) 5.5 m/s
d) 30. m/s
I thought the answer would be 0 m/s because it wouldn't move at the lowest position? However, that's not an answer choice. What is the proper formula to use?
The potential energy at the top is equal to the kinetic energy at the bottom, therefore mgh=.5mv^2. The masses do not matter sense they are equal to each other, so they may be canceled out. You know that the acceleration of gravity is 9.8, so to find the left side--the potential energy-- you do 9.8*1.52. which gives you 14.896. Then you solve for v by isolating the variable. so you multiply by 2 on both sides, then find the square root on both sides. Giving the answer 5.45... or the actual answer C) 5.5 m/s
C. 5.5 m/s
To find the speed of the pendulum at the lowest position, you can use the principle of conservation of energy. The pendulum swings between two extreme points, the highest and lowest positions. At the highest position, all of the potential energy is converted to kinetic energy. At the lowest position, all of the kinetic energy is converted back to potential energy.
The formula we can use to find the speed at the lowest position is:
v = √(2gh)
Where:
v = speed at the lowest position
g = acceleration due to gravity (9.8 m/s^2)
h = maximum height of the pendulum swing (1.52 m)
Plugging in the values, we get:
v = √(2 * 9.8 * 1.52)
v ≈ 3.9 m/s
The correct answer is b) 3.9 m/s.
To find the speed of the pendulum at the lowest position, we can use the principle of conservation of energy. At the highest point, the pendulum has its maximum potential energy, and as it swings down to the lowest position, the potential energy is converted into kinetic energy.
The formula we can use here is the conservation of mechanical energy:
Potential energy (PE) + Kinetic energy (KE) = Total mechanical energy (E)
At the highest point, the potential energy is maximum, and at the lowest point, the potential energy is zero. Therefore, we can write the equation as:
PE + KE = 0 + KE = E
We can calculate the potential energy at the highest point using the formula:
PE = mgh
where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the maximum height (1.52 m).
But since we are only interested in the speed at the lowest position, we can set up the equation as:
mgh = 0 + (1/2)mv²
where v is the velocity/speed at the lowest position.
Simplifying the equation, we find:
mgh = (1/2)mv²
Canceling the mass from both sides of the equation:
gh = (1/2)v²
Rearranging the equation to solve for v:
v² = 2gh
Taking the square root of both sides:
v = √(2gh)
Plugging in the values of g (9.8 m/s²) and h (1.52 m) into the formula:
v = √(2 * 9.8 * 1.52)
v ≈ √(29.792) ≈ 5.457 m/s
Therefore, the speed of the pendulum at the lowest position is approximately 5.457 m/s.
Among the answer choices provided, the closest value is c) 5.5 m/s.