Is this a true and false question?
Answer:
a)
, b)
, c) ![k = 2930.059\,\frac{N}{m}](https://tex.z-dn.net/?f=k%20%3D%202930.059%5C%2C%5Cfrac%7BN%7D%7Bm%7D)
Explanation:
a) The change in the gravitational potential energy of the marble-Earth system is:
![\Delta U_{g} = (0.06\,kg)\cdot \left(9.807\,\frac{m}{s^{2}}\right)\cdot (22\,m)](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bg%7D%20%3D%20%280.06%5C%2Ckg%29%5Ccdot%20%5Cleft%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%5Cright%29%5Ccdot%20%2822%5C%2Cm%29)
![\Delta U_{g} = 12.945\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bg%7D%20%3D%2012.945%5C%2CJ)
b) The change in the elastic potential energy of the spring is equal to the change in the gravitational potential energy, then:
![\Delta U_{k} = 12.945\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%2012.945%5C%2CJ)
c) The spring constant of the gun is:
![\Delta U_{k} = \frac{1}{2} \cdot k \cdot x^{2}](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%20k%20%5Ccdot%20x%5E%7B2%7D)
![k = \frac{2\cdot \Delta U_{k}}{x^{2}}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B2%5Ccdot%20%5CDelta%20U_%7Bk%7D%7D%7Bx%5E%7B2%7D%7D)
![k = \frac{2\cdot (12.945\,J)}{(0.094\,m)^{2}}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B2%5Ccdot%20%2812.945%5C%2CJ%29%7D%7B%280.094%5C%2Cm%29%5E%7B2%7D%7D)
![k = 2930.059\,\frac{N}{m}](https://tex.z-dn.net/?f=k%20%3D%202930.059%5C%2C%5Cfrac%7BN%7D%7Bm%7D)
Below is the solution:
Let us say that the disk goes through a vertical elevation change of one meter.
<span>The change in potential energy will equal the change in kinetic energy </span>
<span>PE = KEt + KEr </span>
<span>mgh = ½mv² + ½Iω² </span>
<span>for a uniform disk, the moment of inertia is </span>
<span>I = ½mr² </span>
<span>and </span>
<span>ω = v/r </span>
<span>mgh = ½mv² + ½(½mr²)(v/r)² </span>
<span>mgh = ½mv² + ¼mv² </span>
<span>gh = ¾v² </span>
<span>v² = 4gh/3 </span>
<span>v² = u² + 2as </span>
<span>if we assume initial velocity is zero </span>
<span>v² = 2as </span>
<span>a = v² / 2s </span>
<span>s(sinθ) = h </span>
<span>s = h/sinθ </span>
<span>a = 4gh/3 / 2(h/sinθ) </span>
<span>a = ⅔gsinθ </span>
<span>a = ⅔(9.8)sin25 </span>
<span>a = 2.8 m/s² </span>
Answer:
Answer is A, it will pass through to focal point after reflecting.
Explanation:
I had the same question in a test, Sorry that you had to do this question in middle school.
Answer:
23.9m
Explanation:
step one:
This problem is on energy.
we can proceed by using the expression for potential energy to solve for height h
we know that
PE=mgh
given that
mass m= 5kg
PE= 1176 joules
step two:
we can substitute our data and find h
1176= 5*9.81*h
1176=49.05h
step three:
divide both sides by 49.05 we have
1176/49.05=h
h=23.9 m
The height of the tree is 23.9m