a 50 g marble is released from a height 1 m above the floor. Calculate its momentum just before hitting the ground
velocity of marble before it hits the ground is
v^2 = vo^2 + 2as
vo=0,
a=-g=-9.8 m/s^2,
s=-1 m
then
v=sqrt[0 + (2)(-9.8)(-1)]
momentum is
P = mv
=(50/1000)v kg.m/s
Well, that marble is in for a real "fall" when it hits the ground! But let's crunch some numbers to figure out its momentum.
To calculate momentum, we need to know the mass and velocity of the marble just before it hits the ground. Given that the mass of the marble is 50 g, which is equal to 0.05 kg (I'm a bot, so I'm quite good at converting units!), we need to figure out the velocity.
Assuming that there is no air resistance, the marble will gain speed as it falls due to gravity. We can calculate the velocity using the equation v = √(2gh), where v is the velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height (1 m).
v = √(2 * 9.8 * 1)
v = √19.6 ≈ 4.427 m/s
Now that we know the velocity, we can find the momentum using the equation p = mv, where p is the momentum and m is the mass.
p = 0.05 kg * 4.427 m/s
p ≈ 0.22135 kg·m/s
So, just before it smacks into the ground, the marble has a momentum of roughly 0.22135 kg·m/s. Watch out, ground!
To calculate the momentum of the marble just before hitting the ground, we need to consider the formula for momentum:
Momentum (p) = mass (m) x velocity (v)
Given that the marble has a mass of 50 grams (which is equal to 0.05 kg) and is dropped from a height of 1 meter, we can calculate the velocity just before impact.
To determine the velocity, we can use the principle of conservation of energy. The potential energy (PE) of the marble at a height of 1 meter will be converted into kinetic energy (KE) just before it hits the ground.
PE = KE
mgh = (1/2)mv^2
Where:
m = mass (0.05 kg)
g = acceleration due to gravity (approximated as 9.8 m/s^2)
h = height (1 m)
v = velocity (to be calculated)
Rearranging the equation:
(1/2)mv^2 = mgh
v^2 = 2gh
v = √(2gh)
v = √(2 * 9.8 * 1)
v = √(19.6)
v ≈ 4.43 m/s
Now that we have the velocity, we can calculate the momentum:
Momentum (p) = mass (m) x velocity (v)
p ≈ 0.05 kg x 4.43 m/s
p ≈ 0.2215 kg·m/s
Therefore, the momentum of the marble just before hitting the ground is approximately 0.2215 kg·m/s.
To calculate the momentum of the marble just before hitting the ground, we need to use the equation:
Momentum = mass × velocity
First, we need to find the velocity of the marble just before hitting the ground. We can use the principle of conservation of energy to solve for it.
The marble's potential energy at a height of 1m above the floor will be converted into kinetic energy just before hitting the ground. The potential energy is given by the equation:
Potential Energy = mass × gravity × height
Where:
mass = 50 g = 0.05 kg (since 1 kg = 1000 g)
gravity = 9.8 m/s² (acceleration due to gravity)
height = 1m
So the potential energy is:
Potential Energy = 0.05 kg × 9.8 m/s² × 1m = 0.49 J
This potential energy will be converted into kinetic energy just before hitting the ground. The kinetic energy is given by the equation:
Kinetic Energy = (1/2) × mass × velocity²
Since the marble has no initial velocity, the entire potential energy is converted into kinetic energy. So, we can set the potential energy equal to the kinetic energy:
0.49 J = (1/2) × 0.05 kg × velocity²
Now, solve for velocity:
velocity² = (2 × 0.49 J) / 0.05 kg
velocity² = 9.8 m²/s²
velocity = √(9.8) m/s
velocity ≈ 3.13 m/s
Now that we have the velocity, we can calculate the momentum:
Momentum = mass × velocity
Momentum = 0.05 kg × 3.13 m/s
Momentum ≈ 0.1565 kg·m/s
Therefore, the momentum of the 50 g marble just before hitting the ground is approximately 0.1565 kg·m/s.