A pile driver of mass 125kg falls through a height of 80m before striking the pile. What is it's momentum at the instance it strikes the pile? g=10m/s2?
V^2 = Vo^2 + 2g*h = 0 + 20*80 = 1600,
V = 40 m/s.
Momentum = M * V ____kg-m/s.
Well, if I were a pile-driving clown, I'd say that the momentum of the pile driver right before it strikes the pile would be a real "crusher"! But let's do some math instead.
The potential energy of the pile driver initially is equal to the work done by gravity as it falls:
Potential energy = mass x gravitational acceleration x height
Potential energy = 125 kg x 10 m/s^2 x 80 m = 100,000 J
Now, since momentum is conserved, this potential energy will be converted into kinetic energy just before it strikes the pile. As they say, "What goes down, must come down even harder!"
Kinetic energy = Potential energy
0.5 x mass x velocity^2 = 100,000 J
Plugging in the values and solving for velocity:
0.5 x 125 kg x velocity^2 = 100,000 J
velocity^2 = (100,000 J) / (0.5 x 125 kg)
velocity^2 = 800 m^2/s^2
velocity ≈ √800 ≈ 28.3 m/s
Now, to find momentum, we just have to multiply the mass by the velocity:
Momentum = mass x velocity
Momentum = 125 kg x 28.3 m/s
Momentum ≈ 3,538.75 kg·m/s
So, the momentum of the pile driver at the instant it strikes the pile would be approximately 3,538.75 kg·m/s. That's one heavy hitter!
To calculate the momentum of the pile driver at the instance it strikes the pile, we need to use the equation:
Momentum = mass × velocity
First, let's calculate the final velocity of the pile driver right before it strikes the pile. Since the pile driver falls freely under gravity, we can use the equation:
Potential energy = mass × gravity × height
Here, the potential energy is converted into the kinetic energy of the pile driver, given by:
Kinetic energy = (1/2) × mass × velocity^2
Equating the potential energy and kinetic energy equations, we have:
mass × gravity × height = (1/2) × mass × velocity^2
Simplifying the equation, we get:
gravity × height = (1/2) × velocity^2
Since gravity (g) is given as 10 m/s² and the height (h) is given as 80 m, we can substitute these values into the equation to solve for velocity:
10 m/s² × 80 m = (1/2) × velocity^2
800 m²/s² = velocity^2
Taking the square root of both sides, we find:
velocity ≈ √(800 m²/s²) ≈ 28.28 m/s
Now, we can calculate the momentum using the mass and the velocity:
Momentum = mass × velocity
= 125 kg × 28.28 m/s
≈ 3535 kg·m/s
Therefore, the momentum of the pile driver at the instance it strikes the pile is approximately 3535 kg·m/s.
To calculate the momentum of the pile driver at the instance it strikes the pile, we need to use the formula:
Momentum = mass × velocity
First, we need to find the velocity of the pile driver just before it strikes the pile. We can use the concept of conservation of energy to do this.
The potential energy of the pile driver when it is at a height of 80m is given by the formula:
Potential energy = mass × gravity × height
Substituting the given values into the equation, we have:
Potential energy = 125 kg × 10 m/s^2 × 80 m
= 100,000 J
This potential energy is converted into kinetic energy just before the pile driver strikes the pile. The kinetic energy formula is:
Kinetic energy = (1/2) × mass × velocity^2
Since the potential energy is converted entirely into kinetic energy, we can equate the two:
Kinetic energy = Potential energy
(1/2) × mass × velocity^2 = 100,000 J
From this equation, we can solve for velocity:
velocity = √[(2 × Potential energy) / mass]
velocity = √[(2 × 100,000 J) / 125 kg]
= √[1600 m^2/s^2]
= 40 m/s
Now that we have the velocity, we can calculate the momentum:
Momentum = mass × velocity
= 125 kg × 40 m/s
= 5000 kg·m/s
Therefore, the momentum of the pile driver at the instance it strikes the pile is 5000 kg·m/s.