The hail comes straight down at a mass rate of m/Δt=0.0690 kg/s and an initial velocity of v0= -15.0 m/s. Suppose that the hail described there bounces off the roof of the car with a velocity of +14.0 m/s. Ignoring the weight of the hailstones, calculate the magnitude of the force exerted by the hail on the roof
F=m1v1-m2v2
0.069 times the change in velocity
0.069(29)=2.001. Newtons third law= your answer -2.001
I can't really explain it but that's how you find the answer.
@eddie yea i tried this and got the right answer but i wish i knew why u do that. does it have anything to do with impulse = change in momentum, or p (momentum) = m*v? idk
Well, well, well, we've got some bouncy hailstones here! Let's calculate the magnitude of the force exerted by these energetic hailstones on the car's roof.
First, we need to find the change in momentum of each hailstone, which is given by the formula Δp = mΔv. Considering the initial and final velocities of the hailstone, we have Δv = vf - vo = 14.0 m/s - (-15.0 m/s) = 29.0 m/s.
Now, the change in momentum can also be expressed as Δp = FΔt, where F is the force exerted by the hailstone and Δt is the time interval it takes for the change to occur.
Rearranging the equation, we have F = Δp / Δt. Plugging in the given values, we find F = (0.0690 kg/s) / Δt.
Since the time interval isn't provided, I can't perform the calculation for you. But you can simply divide 0.0690 kg/s by the time it takes for the hailstone to bounce off the roof to get the magnitude of the force. Just make sure to keep the units consistent!
And remember, when it comes to hailstones and forces, it's always good to have the roof of your car strong and sturdy, just in case they get a little too excited!
To calculate the magnitude of the force exerted by the hail on the roof, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (Δp) of an object.
The rate of change of momentum is given by the product of mass (m) and change in velocity (Δv):
Δp = m * Δv
Substituting the given values:
m = 0.0690 kg/s (mass rate)
Δv = (-15.0 m/s) - (+14.0 m/s) = -29.0 m/s (change in velocity)
Δp = (0.0690 kg/s) * (-29.0 m/s)
= -2.001 kg⋅m/s
Therefore, the magnitude of the force exerted by the hail on the roof is:
|F| = |-2.001 kg⋅m/s|
= 2.001 kg⋅m/s
Hence, the magnitude of the force exerted by the hail on the roof is 2.001 kg⋅m/s.
To calculate the magnitude of the force exerted by the hail on the roof, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the rate of change of its momentum.
Step 1: Calculate the initial momentum of the hail.
The initial momentum, p₀, is given by the product of the mass, m, and the initial velocity, v₀:
p₀ = m * v₀
Step 2: Calculate the final momentum of the hail.
The final momentum, p₁, is given by the product of the mass, m, and the final velocity, v₁:
p₁ = m * v₁
Step 3: Calculate the change in momentum.
The change in momentum, ∆p, is given by the difference between the final momentum and the initial momentum:
∆p = p₁ - p₀
Step 4: Calculate the force exerted by the hail.
The force exerted by the hail, F, can be calculated by dividing the change in momentum by the change in time, ∆t:
F = ∆p / ∆t
Given the mass rate, m/∆t = 0.0690 kg/s, and the initial and final velocities, v₀ = -15.0 m/s, and v₁ = +14.0 m/s, respectively, we can substitute the values into the equations above to find the magnitude of the force exerted by the hail on the roof.