An object is thrown straight upwards from the ground at 28 m/s. Due to air resistance (a non-conservative force), the object loses 31.4 percent of its initial energy during its trip to reach maximum height. How much higher does the object travel if there was no air resistance? Answer in meters.
Vo = 28m/s with no air resistance.
h1 = (Vf^2 - Vo^2) / 2g,
h1 = (0 - (28)^2) / -19.6 = 40m.
Vo = 28 * (100%-31.4%)/100% = 18.452m/s
with air res.
h2 = (0 - (18.452)^2) / -19.6 = 17.4m.
h=hi - h2 = 40 - 17.4 = 22.63m. higher
with no air res.
To find out how much higher the object would travel without air resistance, we need to compare its initial kinetic energy to the potential energy at its maximum height. We can assume that the loss of energy due to air resistance is equal to the loss of potential energy at the maximum height.
First, let's find the initial kinetic energy (KE_initial) of the object. The formula for kinetic energy is:
KE = (1/2) * m * v^2
where m is the mass of the object and v is the velocity.
Given that the object is thrown straight upwards, we can assume its mass doesn't change during the flight. Therefore, we can focus on the velocity.
The initial velocity (v_initial) of the object is given as 28 m/s.
Now, we can calculate the initial kinetic energy (KE_initial):
KE_initial = (1/2) * m * v_initial^2
Next, let's find the potential energy at the maximum height. The formula for potential energy is:
PE = m * g * h
where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
We want to find the increase in height when air resistance is absent. Let's call this height difference Δh.
Since the energy loss due to air resistance is given as a percentage of the initial energy, we can write this as:
Δh = (1 - 31.4%) * h
Therefore, we need to find h to determine the increase in height.
We can equate the loss of energy to the loss of potential energy:
(1 - 31.4%) * KE_initial = m * g * Δh
Rearranging the equation:
Δh = [(1 - 31.4%) * KE_initial] / (m * g)
Now we can substitute the values given into the equation to find Δh:
Δh = [(1 - 0.314) * KE_initial] / (m * g)
Since we are only interested in the increase in height, the Δ symbolizes the change in height. The final height is the sum of the change in height and the initial height:
Final Height = (Initial Height) + Δh
Please provide the mass of the object so that I can provide you with an accurate answer.