Answer:
114.44 J
Explanation:
From Hook's Law,
F = ke................. Equation 1
Where F = Force required to stretch the spring, k = spring constant, e = extension.
make k the subject of the equation
k = F/e.............. Equation 2
Given: F = 10 lb = (10×4.45) N = 44.5 N, e = 4 in = (4×0.254) = 1.016 m.
Substitute into equation 2
k = 44.5/1.016
k = 43.799 N/m
Work done in stretching the 9 in beyond its natural length
W = 1/2ke²................. Equation 3
Given: e = 9 in = (9×0.254) = 2.286 m, k = 43.799 N/m
Substitute into equation 3
W = 1/2×43.799×2.286²
W = 114.44 J
<span>K.E = 0.5 * m * v^2 ( m = mass(Kg), V = Velocity(m/s)
= 0.5 * 8 * 5^2
= 4 * 25
= 100 J </span>
Answer:
![F_0 = 393 N](https://tex.z-dn.net/?f=F_0%20%3D%20393%20N)
Explanation:
As we know that amplitude of forced oscillation is given as
![A = \frac{F_0}{ m(\omega^2 - \omega_0^2)}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7BF_0%7D%7B%20m%28%5Comega%5E2%20-%20%5Comega_0%5E2%29%7D)
here we know that natural frequency of the oscillation is given as
![\omega_0 = \sqrt{\frac{k}{m}}](https://tex.z-dn.net/?f=%5Comega_0%20%3D%20%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D)
here mass of the object is given as
![m = \frac{W}{g}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7BW%7D%7Bg%7D)
![\omega_0 = \sqrt{\frac{220}{\frac{30}{9.81}}}](https://tex.z-dn.net/?f=%5Comega_0%20%3D%20%5Csqrt%7B%5Cfrac%7B220%7D%7B%5Cfrac%7B30%7D%7B9.81%7D%7D%7D)
![\omega_0 = 8.48 rad/s](https://tex.z-dn.net/?f=%5Comega_0%20%3D%208.48%20rad%2Fs)
angular frequency of applied force is given as
![\omega = 2\pi f](https://tex.z-dn.net/?f=%5Comega%20%3D%202%5Cpi%20f)
![\omega = 2\pi(10.5) = 65.97 rad/s](https://tex.z-dn.net/?f=%5Comega%20%3D%202%5Cpi%2810.5%29%20%3D%2065.97%20rad%2Fs)
now we have
![0.03 = \frac{F_0}{3.06(65.97^2 - 8.48^2)}](https://tex.z-dn.net/?f=0.03%20%3D%20%5Cfrac%7BF_0%7D%7B3.06%2865.97%5E2%20-%208.48%5E2%29%7D)
![F_0 = 393 N](https://tex.z-dn.net/?f=F_0%20%3D%20393%20N)
Answer:
the kinetic energy lost due to friction is 22.5 J
Explanation:
Given;
mass of the block, m = 0.2 kg
initial velocity of the block, u = 25 m/s
final velocity of the block, v = 20 m/s
The kinetic energy lost due to friction is calculated as;
![\Delta K.E= K.E_f - K.E_i\\\\\Delta K.E= \frac{1}{2}mv^2 - \frac{1}{2}mu^2\\\\\Delta K.E= \frac{1}{2}m(v^2 -u^2)\\\\\Delta K.E= \frac{1}{2} \times 0.2 (20^2 - 25^2)\\\\\Delta K.E= -22.5 \ J](https://tex.z-dn.net/?f=%5CDelta%20K.E%3D%20K.E_f%20-%20K.E_i%5C%5C%5C%5C%5CDelta%20K.E%3D%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20-%20%20%5Cfrac%7B1%7D%7B2%7Dmu%5E2%5C%5C%5C%5C%5CDelta%20K.E%3D%20%5Cfrac%7B1%7D%7B2%7Dm%28v%5E2%20-u%5E2%29%5C%5C%5C%5C%5CDelta%20K.E%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%200.2%20%2820%5E2%20-%2025%5E2%29%5C%5C%5C%5C%5CDelta%20K.E%3D%20-22.5%20%5C%20J)
Therefore, the kinetic energy lost due to friction is 22.5 J
It’s c.) I think so at least