An animal-rescue plane flying due east at 36.0 m/s drops a bale of hay from an altitude of h = 69.5 m, as shown below. If the bale of hay weighs F = 162 N, what is the momentum of the bale the moment before it strikes the ground? Give both magnitude and direction.
weight=mg
mg*h= GPE(initial)=KE(final)=1/2mv^2
(2*mgh)^1/2=mv=momentum=(2*(162N)(69.5m))^1/2= 150 N s
To find the momentum of the bale of hay just before it strikes the ground, we can use the equation:
momentum = mass × velocity
However, we need to find the velocity of the bale before we can calculate its momentum.
The initial velocity of the bale is the same as the velocity of the rescue plane, since it was dropped vertically from the plane. We are given that the plane is flying due east at 36.0 m/s, so the initial velocity of the bale is also 36.0 m/s due east.
To find the final velocity of the bale when it strikes the ground, we can use the equations of motion for freefall. Since the bale was dropped vertically, we can ignore any horizontal motion and focus only on its vertical motion.
The equation to use in this case is:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity
a = acceleration due to gravity (approximately 9.8 m/s^2)
s = displacement (in this case, the vertical distance h = 69.5 m)
Now, let's calculate the final velocity of the bale:
v^2 = u^2 + 2as
v^2 = (36.0 m/s)^2 + 2(-9.8 m/s^2)(69.5 m)
v^2 = 1296 m^2/s^2 - 1364.4 m^2/s^2
v^2 = -68.4 m^2/s^2
Since the velocity cannot be negative in magnitude, we take the positive square root:
v = √(68.4 m^2/s^2)
v ≈ 8.275 m/s
Now that we have the velocity of the bale just before it strikes the ground, we can calculate its momentum:
momentum = mass × velocity
momentum = 162 N ÷ 9.8 m/s^2 × 8.275 m/s
Calculating this:
momentum ≈ 1440.43 N·s
Therefore, the momentum of the bale just before it strikes the ground is approximately 1440.43 N·s. The direction of the momentum is downward, since the bale is falling vertically towards the ground.
To calculate the momentum of the bale of hay just before it strikes the ground, we need to use the equation:
Momentum = mass × velocity
First, we need to find the mass of the bale of hay. We can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
Force = mass × acceleration
In this case, the force is given and equals 162 N. We also know the acceleration due to gravity, which is approximately 9.8 m/s². So we can rearrange the equation to solve for mass:
mass = Force / acceleration
mass = 162 N / 9.8 m/s²
mass ≈ 16.53 kg (rounded to two decimal places)
Now that we have the mass of the bale of hay, we can calculate the momentum by multiplying the mass by the velocity. In this case, the velocity is given as 36.0 m/s.
Momentum = mass × velocity
Momentum = 16.53 kg × 36.0 m/s
Momentum ≈ 595.08 kg·m/s (rounded to two decimal places)
So the magnitude of the momentum of the bale of hay just before it strikes the ground is approximately 595.08 kg·m/s.
To determine the direction of the momentum, we need to consider that the animal-rescue plane is flying due east. Since the bale of hay is dropped from the plane, it will continue moving in the same direction as the plane until it hits the ground. Therefore, the direction of the momentum is east.
So, the momentum of the bale of hay just before it strikes the ground is approximately 595.08 kg·m/s in the east direction.