Find the momentum of a 30.g stone that starts from rest and falls to the ground from a height of 20.m.
we want the speed times the mass.
a = -9.81 m/s^2
v = 0 - 9.81 t
h = 20 -9.81/2 t^2 = 20 - 4.9 t^2
h = 0 at ground so
4.9 t^2 = 20
then go back and use that t
v = -9.81 t
then finally
P = momentum = m v = 0.030 * v
V^2 = Vo^2 + 2g*h = 0 + 19.6 * 20 = 392.
V = 19.8 m/s.
Momentum = M * V = 0.03 * V.
To find the momentum of the stone, we need to use the formula:
Momentum (p) = mass (m) x velocity (v)
First, we need to determine the final velocity of the stone when it hits the ground. We can do this by using the principle of conservation of energy. We know that the potential energy of an object at height h is given by:
Potential energy (PE) = mass (m) x acceleration due to gravity (g) x height (h)
In this case, the potential energy is converted to kinetic energy when the stone falls to the ground. Therefore, we can equate the potential energy to the kinetic energy:
Potential energy (PE) = Kinetic energy (KE)
mgh = (1/2)mv^2
where m is the mass of the stone, g is the acceleration due to gravity (9.8 m/s^2), h is the height (20 m), and v is the final velocity.
Simplifying the equation, we have:
mgh = (1/2)mv^2
Dividing both sides of the equation by m, we have:
gh = (1/2)v^2
Solving for v, we get:
v^2 = 2gh
Taking the square root of both sides, we find:
v = √(2gh)
Now, substituting the known values, we have:
v = √(2 * 9.8 m/s^2 * 20 m)
= √(392 m^2/s^2)
≈ 19.80 m/s
Now that we have the final velocity, we can calculate the momentum using the formula:
Momentum (p) = mass (m) x velocity (v)
Since the mass of the stone is given as 30 g, we need to convert it to kilograms:
mass (m) = 30 g = 0.030 kg
Now, substituting the values into the formula, we find:
Momentum (p) = 0.030 kg * 19.80 m/s
≈ 0.594 kg·m/s
Therefore, the momentum of the stone is approximately 0.594 kg·m/s.