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 kinetic energy of the merry-goround after 3.62 s is 544J
Explanation:
Given :
Weight w = 745 N
Radius r = 1.45 m
Force = 56.3 N
To Find:
The kinetic energy of the merry-go round after 3.62 = ?
Solution:
Step 1: Finding the Mass of merry-go-round
m = 76.02 kg
Step 2: Finding the Moment of Inertia of solid cylinder
Moment of Inertia of solid cylinder I =
Substituting the values
Moment of Inertia of solid cylinder I
=>
=>
=>
Step 3: Finding the Torque applied T
Torque applied T =
Substituting the values
T =
T = 81.635 N.m
Step 4: Finding the Angular acceleration
Angular acceleration ,
Substituting the values,
Step 4: Finding the Final angular velocity
Final angular velocity ,
Substituting the values,
Now KE (100% rotational) after 3.62s is:
KE =
KE =
KE = 544J
Power is defined by the rate of work done by the object. Statement D represents the correct definition of Power.
<h3>What is Power?</h3>Power can be defined as the transfer of energy from one place to another place. The rate at which this energy is transferred is called power.
In other words, the rate at which the work is done by an object is called its power. The mathematical representation of power is given as,
Here, P is the power, is the change in energy or work done and
change in time.
The Power can be written in SI units as Watt or J/s.
Hence we can conclude that the power is the rate at which work is accomplished. Statement D is the correct representation of Power.
To know more about power, follow the link given below.