A small bag of sand is released from an ascending hot-air balloon whose upward constant velocity is v0 = 2.45 m/s. knowing that
at the time of the release the balloon was 98.8 m above the ground, determine the time, τ, it takes the bag to reach the ground from the moment of its release.
1 answer:
When you draw an illustration for this problem, you would come up with the same drawing as shown in the picture. As the hot-air balloon travels upwards, there is a slight time when the bag of sand rises up until it reaches the maximum height. Then, it goes back down to the ground. The total time would be t₁ + t₂. The solution is as follows:
H = v₀²/2g = (2.45)²/2(9.81) = 0.306 m
t₁ = H/v₀ = 0.306 m/2.45 m/s = 0.125 s
t₂ = √2(H + 98.8)/g = √2(0.306+ 98.8)/9.81
t₂ = 4.495 s
Total time = 0.125 s + 4.495 s = 4.62 seconds
H = v₀²/2g = (2.45)²/2(9.81) = 0.306 m
t₁ = H/v₀ = 0.306 m/2.45 m/s = 0.125 s
t₂ = √2(H + 98.8)/g = √2(0.306+ 98.8)/9.81
t₂ = 4.495 s
Total time = 0.125 s + 4.495 s = 4.62 seconds
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Answer:
The work done on the system can be accounted for by;
Both and
Explanation:
The speed of the crate = Constant
Therefore, the acceleration of the crate = 0 m/s²
The net force applied to the crate, = 0
Therefore, the force of with which the crate is pulled = The force resisting the upward motion of the crate
However, we have;
The force resisting the upward motion of the crate = The weight of the crate + The frictional resistance of the ramp due to the surface contact between the ramp and the crate
The work done on the system = The energy to balance the resisting force = The weight of the crate × The height the crate is raised + The heat generated as internal energy to the system
The weight of the crate × The height the crate is raised = Gravitational Potential Energy =
The heat generated as internal energy to the system =
Therefore;
The work done on the system = +
.
To solve this problem, we will start by defining each of the variables given and proceed to find the modulus of elasticity of the object. We will calculate the deformation per unit of elastic volume and finally we will calculate the net energy of the system. Let's start defining the variables
Yield Strength of the metal specimen
Yield Strain of the Specimen
Diameter of the test-specimen
Gage length of the Specimen
Modulus of elasticity
Strain energy per unit volume at the elastic limit is
Considering that the net strain energy of the sample is
Therefore the net strain energy of the sample is