A body of mass 4 kg is dropped from a height of 20m .calculate the initial momentum and the momentum just before it strikes the ground (g=10m/s*s)
if v = 0, p = 0
v ground = sqrt (2 g h)
momentum at ground = m v = 4 sqrt (2 g h)
To calculate the initial momentum of the body, we can use the equation:
Initial momentum = mass x initial velocity
Given:
Mass (m) = 4 kg
The body is dropped from a height of 20 m, which means it starts with zero initial velocity because it's not thrown. Therefore, the initial momentum is:
Initial momentum = 4 kg x 0 m/s = 0 kg*m/s
Next, let's calculate the momentum just before it strikes the ground. We need to use the principle of conservation of energy since this is a free-fall motion.
The potential energy at the highest point (when it is dropped) will be equal to kinetic energy at the lowest point (when it strikes the ground). This can be represented by the equation:
Potential energy = Kinetic energy
The potential energy is given by:
Potential energy = mass x gravity x height
Given:
Mass (m) = 4 kg
Gravity (g) = 10 m/s^2
Height (h) = 20 m
Potential energy = 4 kg x 10 m/s^2 x 20 m = 800 J
Since the potential energy is equal to the kinetic energy just before hitting the ground, we have:
Kinetic energy = 800 J
The kinetic energy is given by:
Kinetic energy = (1/2) x mass x velocity^2
Since we want to find the momentum just before it strikes the ground, we can use the equation:
P = m x v
Solving for velocity, we have:
Velocity = √(2 x kinetic energy / m)
Substituting the values, we get:
Velocity = √(2 x 800 J / 4 kg) = √(400 J / kg) = 20 m/s
Finally, the momentum just before it strikes the ground is:
Momentum = mass x velocity = 4 kg x 20 m/s = 80 kg*m/s
So, the initial momentum is 0 kg*m/s and the momentum just before it strikes the ground is 80 kg*m/s.
To calculate the initial momentum, we need to multiply the mass of the body by its initial velocity.
Since the body is dropped from rest, the initial velocity is 0 m/s. Therefore, the initial momentum is:
Initial momentum = mass × initial velocity
Initial momentum = 4 kg × 0 m/s
Initial momentum = 0 kg⋅m/s (since anything multiplied by 0 is 0)
Next, let's calculate the final momentum just before the body strikes the ground.
We can use the equation for the final velocity (v) of an object when it is dropped from a height:
v = √(2gh)
Where:
v = final velocity
g = acceleration due to gravity (10 m/s²)
h = height (20 m in this case)
Plugging in the values:
v = √(2 × 10 m/s² × 20 m)
v = √(400 m²/s²)
v = 20 m/s
Now that we have the final velocity, we can calculate the final momentum. Since the mass of the body remains the same:
Final momentum = mass × final velocity
Final momentum = 4 kg × 20 m/s
Final momentum = 80 kg⋅m/s
Therefore, the initial momentum is 0 kg⋅m/s, and the momentum just before it strikes the ground is 80 kg⋅m/s.