Calculate the potential energy stored in a metal ball of a mass of 80 kg kept at a height of 15m from the earth surface.What wil
2 answers:
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Answer:
A. xmax = 131.49 m
B. t = 8.74 s
C. ymax = 220.33 m
Explanation:
A. In order to find the horizontal distance which cannon travels you first calculate the flight time. The flight time can be calculated by using the following formula:
(1)
yo: height from the projectile is fired = 200m
vo: initial velocity of the projectile = 25m/s
g: gravitational acceleration = 9.8 m/s^2
θ: angle between the direction of the initial motion of the ball and the horizontal = 53°
t: time
You need the value of t when the projectile hits the ground. Then, in th equation (1) you make y = 0m.
When you replace the values of all parameters in the equation (1), you obtain the following quadratic formula:
(2)
You use the quadratic formula to obtain the value of t:
You use the positive value because it has physical meaning.
Now, you can calculate the horizontal range of the projectile by using the following formula:
The cannon ball travels a horizontal distance of 131.49 m
B. The cannon ball reaches the canon for t = 8.74s
C. The maximum height is obtained by using the following formula:
(3)
By replacing in the equation (3) the values of all parameters you obtain:
The maximum height reached by the cannon ball is 220.33m
Answer:
- <u><em>1. Part A: 648N</em></u>
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- <u><em>2. Part B: 324J</em></u>
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- <u><em>3. Part C: 1,296N</em></u>
Explanation:
<em><u>1. Part A:</u></em>
The magnitude of the force is calculated using the Hook's law:
You know but you do not have
.
You can calculate it using the equation for the work-energy for a spring.
The work done to compress the springs a distance is:
Where is the change in the elastic potential energy of the "spring".
Here you have two springs, but you can work as if they were one spring.
You know the work (81.0J) and the length the "spring" was compressed (0.250m). Thus, just substitute and solve for k:
In reallity, the constant of each spring is half of that, but it is not relevant for the calculations and you are safe by assuming that it is just one spring with that constant.
Now calculate the magnitude of the force:
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<u><em>2. Part B. How much additional work must you do to move the platform a distance 0.250 m farther?</em></u>
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The additional work will be the extra elastic potential energy that the springs earn.
You already know the elastic potential energy when Δx = 0.250m; now you must calculate the elastic potential energy when Δx = 0.250m + 0.250m = 0.500m.
Therefore, you must do 324J of additional work to move the plattarform a distance 0.250 m farther.
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<em><u>3. Part C</u></em>
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<u><em>What maximum force must you apply to move the platform to the position in Part B?</em></u>
The maximum force is when the springs are compressed the maximum and that is 0.500m
Therefore, use Hook's law again, but now the compression length is Δx = 0.500m