A body of mass four kg is dropped from a height of 20m. Calculate the initial momentum and the momentum just before it strikes the ground.
To calculate the initial momentum and the momentum just before the body strikes the ground, you can use the momentum equation:
Momentum = mass x velocity
Let's solve this step-by-step:
1. Determine the mass of the body: The body's mass is given as 4 kg.
2. Calculate the gravitational potential energy (GPE) of the body at a height of 20 m:
GPE = mass x acceleration due to gravity x height
= 4 kg x 9.8 m/s^2 x 20 m
= 784 J (Joules)
3. Use the principle of conservation of energy to find the final velocity just before it strikes the ground:
GPE = kinetic energy (KE)
784 J = (1/2) x mass x velocity^2
Rearrange the equation to solve for velocity:
velocity^2 = (2 x GPE) / mass
velocity^2 = (2 x 784 J) / 4 kg
velocity^2 = 1568 J / 4 kg
velocity^2 = 392 m^2/s^2
Take the square root of both sides to find the velocity:
velocity = √392 m^2/s^2
velocity ≈ 19.8 m/s
4. Calculate the initial momentum:
Initial momentum = mass x initial velocity
Since the body is dropped from rest, the initial velocity is zero.
Therefore, the initial momentum = 4 kg x 0 m/s
Initial momentum = 0 kg⋅m/s
5. Calculate the momentum just before the body strikes the ground:
Momentum just before striking the ground = mass x velocity
Momentum = 4 kg x 19.8 m/s
Momentum ≈ 79.2 kg⋅m/s
So, the initial momentum is 0 kg⋅m/s, and the momentum just before the body strikes the ground is approximately 79.2 kg⋅m/s.
To calculate the initial momentum, we need to determine the velocity of the body just before it is dropped. We can use the equation:
v = √(2gh)
where:
v is the velocity,
g is the acceleration due to gravity (which is approximately 9.8 m/s²),
and h is the height (20m).
Plugging in these values, we get:
v = √(2 * 9.8 * 20) = √(392) ≈ 19.8 m/s
Now, we can calculate the initial momentum (P) using the formula:
P = mv
where:
m is the mass of the body (4 kg),
and v is the velocity (19.8 m/s).
So the initial momentum (P) is:
P = 4 kg * 19.8 m/s ≈ 79.2 kg·m/s
To calculate the momentum just before the body strikes the ground, we need to consider that the body will have the same mass but will be moving with a different velocity. The velocity just before it strikes the ground will be its terminal velocity, which is calculated using the equation:
v² = u² + 2gh
where:
v is the final velocity just before hitting the ground (also the same as terminal velocity),
u is the initial velocity (19.8 m/s),
g is the acceleration due to gravity (9.8 m/s²),
and h is the height (20m).
Plugging in these values, we can solve for v:
v² = (19.8 m/s)² + 2 * 9.8 m/s² * 20m
v² = 392 + 392
v² = 784
v ≈ √784 ≈ 28 m/s
Finally, we can calculate the momentum just before it strikes the ground using:
P = mv
where:
m is the mass of the body (4 kg),
and v is the final velocity just before it hits the ground (28 m/s).
So, the momentum just before it strikes the ground (P) is:
P = 4 kg * 28 m/s ≈ 112 kg·m/s
Therefore, the initial momentum is approximately 79.2 kg·m/s and the momentum just before it strikes the ground is approximately 112 kg·m/s.
initial p = mv = 0
Final v = √(2*9.8*20)
So now you can figure the final p