A 3.4 kg mass is shot by a sling shot with an initial velocity of 4.5 m/s. When the mass is in the air at a height of 50m, it is still traveling upwards. What is its velocity at that height? Draw energy pie graphs for the initial and final state. (Hint: You will have to use conservation of energy and there may be more than one energy on one of the sides)
To find the velocity of the mass at a height of 50m, we can use the principle of conservation of energy. At this height, the mass has both potential energy and kinetic energy. The total mechanical energy (E) of the system is conserved, so we can equate the initial and final energy states.
The initial energy state consists of only kinetic energy because the mass is on the ground and has not gained any potential energy yet. The final energy state consists of both kinetic energy and potential energy because the mass is at a height of 50m.
Using the equation for kinetic energy (KE) and potential energy (PE), we have:
Initial Energy = Final Energy
(1/2)mv^2 = mgh
Where:
m = mass of the object (3.4 kg)
v = velocity of the object
g = acceleration due to gravity (9.8 m/s^2)
h = height (50m)
Solving for v in the above equation:
(1/2) * 3.4 * v^2 = 3.4 * 9.8 * 50
Next, we can simplify the equation:
(1/2) * v^2 = 9.8 * 50
Now, we can solve for v:
v^2 = (9.8 * 50) / (1/2)
v^2 = 490
v = √490
Therefore, the velocity of the mass at a height of 50m is approximately 22.14 m/s.
Now, let's draw energy pie graphs for the initial and final states to visualize the energy distribution.
Initial State (Ground)
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| Kinetic Energy |
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Final State (Height = 50m)
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| Kinetic Energy |
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| Potential Energy |
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In the initial state, all the energy is in the form of kinetic energy because the mass is not yet at any height and does not have any potential energy.
In the final state, the energy is distributed between kinetic energy and potential energy. The mass has reached a height of 50m and gained potential energy, but it still has some kinetic energy as it is still moving upward.