A pile driver falls a distance of 1.75 m before hitting a pile. Find its velocity as it hits
the pile.
So its 1.75x9.80=17.15?
V^2 = Vo^2 + 2g*h = 0 + 19.6*1.75 = 34.3
V = 5.86 m/s.
Note: Always show your Eq before plugging in the values.
Well, if the pile driver is having a bad day and falls 1.75 meters, we'll need to understand gravity's role in the situation. Gravity makes things fall at a rate of about 9.8 meters per second per second. So if we multiply 1.75 by 9.8, we get a value of 17.15. But hold on, that's not the velocity just yet!
Velocity is a measure of speed with a direction, and we need to consider that the pile driver is falling downwards. So technically, its velocity as it hits the pile would be negative. Let's say it has a velocity of -17.15 meters per second. That would be more accurate, but boy oh boy, I hope that pile is ready to be hit!
To find the velocity of the pile driver as it hits the pile, we need to use the principle of conservation of energy.
The potential energy of the pile driver when it is at a height of 1.75 m can be calculated using the formula PE = mgh, where m is the mass of the pile driver, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
Let's assume the mass of the pile driver is m kg.
Therefore, the potential energy is given by PE = m * g * h = m * 9.8 * 1.75.
Now, according to the law of conservation of energy, the potential energy will be converted into kinetic energy just before the pile driver hits the pile.
The kinetic energy (KE) of an object with mass m moving with velocity v can be calculated using the formula KE = 0.5 * m * v^2.
Since the potential energy is converted into kinetic energy, we can equate the two expressions:
PE = KE
m * 9.8 * 1.75 = 0.5 * m * v^2.
Simplifying this equation, we have:
17.15 * m = 0.5 * m * v^2.
Dividing by m on both sides, we get:
17.15 = 0.5 * v^2.
Now, rearranging the equation to solve for v:
v^2 = 17.15 * 2.
v^2 = 34.3.
Taking the square root of both sides, we get:
v = √34.3.
So, the velocity of the pile driver as it hits the pile is approximately equal to √34.3 m/s.
To find the velocity of the pile driver as it hits the pile, you need to use the concept of conservation of energy.
When the pile driver falls, it loses potential energy and gains kinetic energy. The potential energy lost is given by the formula:
Potential energy = mass × gravity × height
Assuming the mass of the pile driver is known, and gravity is approximately equal to 9.8 m/s², you can calculate the potential energy lost.
Then, using the principle of conservation of energy, the lost potential energy is equal to the gained kinetic energy. The kinetic energy is given by the formula:
Kinetic energy = 0.5 × mass × velocity^2
Now you can set up the equation:
Potential energy lost = Kinetic energy
Therefore,
(mass × gravity × height) = 0.5 × mass × velocity^2
In this case, you know that the height is 1.75 m. Rearranging the equation and solving for velocity, you get:
velocity = √(2 × gravity × height)
Substituting the known values into the equation:
velocity = √(2 × 9.8 m/s² × 1.75 m)
Evaluating the expression:
velocity ≈ √(34.3 m²/s²)
velocity ≈ 5.86 m/s
So, the velocity of the pile driver as it hits the pile is approximately 5.86 m/s.