Answer:
9000RPM
Explanation:
"Angular velocity" is directly related to kinetic energy, that is, the Kinetic energy equation would allow an approximation to the resolution investigated in the problem.
The equation for KE is given by:
![KE = \frac{1}{2} lw ^ 2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20lw%20%5E%202)
Now, starting from there towards the <em>Angular equation of kinetic energy</em>, the moment of inertia (i) is used instead of mass (m), and angular velocity (w) instead of linear velocity (V)
That's how we get
![KE_{Angular} = \frac{1}{2} Iw^2](https://tex.z-dn.net/?f=KE_%7BAngular%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20Iw%5E2)
calculating the inertia for a solid cylindrical disk, of
m = 400kg
r = 1.2 / 2 = 0.6m
![I_{disk} = \frac{1}{2} mr^2 = (0.5) (400) (0.6)^2 = 72 kgm^2](https://tex.z-dn.net/?f=I_%7Bdisk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mr%5E2%20%3D%20%280.5%29%20%28400%29%20%280.6%29%5E2%20%3D%2072%20kgm%5E2)
We understand that the total kinetic energy is 3.2 * 10 ^ 7J, like this:
![3.2*10^7 = \frac{1}{2} Iw^2 = (0.5) (72) w^2 = 36w^2](https://tex.z-dn.net/?f=3.2%2A10%5E7%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20Iw%5E2%20%3D%20%280.5%29%20%2872%29%20w%5E2%20%3D%2036w%5E2)
![w^2 = 3.2*10^7 / 36 = 0.0888*10^7 = 88.8*10^4](https://tex.z-dn.net/?f=w%5E2%20%3D%203.2%2A10%5E7%20%2F%2036%20%3D%200.0888%2A10%5E7%20%3D%2088.8%2A10%5E4)
![w = 9.43*10^2 = 943 rad / s](https://tex.z-dn.net/?f=w%20%3D%209.43%2A10%5E2%20%3D%20943%20rad%20%2F%20s)
Thus,
943 rad / s ≈ 9000 rpm
The distance traveled by the hockey player is 0.025 m.
<h3>The principle of conservation of linear momentum;</h3>
- The principle of conservation of linear momentum states that, the total momentum of an isolated system is always conserved.
The final velocity of the hockey play is calculated by applying the principle of conservation of linear momentum;
![m_1v_1 = m_2 v_2\\\\v_1 = \frac{m_2 v_2}{m_1} \\\\v_1 = \frac{0.150 \times 45}{90} \\\\v_1 = 0.075 \ m/s](https://tex.z-dn.net/?f=m_1v_1%20%3D%20m_2%20v_2%5C%5C%5C%5Cv_1%20%3D%20%5Cfrac%7Bm_2%20v_2%7D%7Bm_1%7D%20%5C%5C%5C%5Cv_1%20%3D%20%5Cfrac%7B0.150%20%5Ctimes%2045%7D%7B90%7D%20%5C%5C%5C%5Cv_1%20%3D%200.075%20%5C%20m%2Fs)
The time taken for the puck to reach 15 m is calculated as follows;
![t = \frac{d}{v} \\\\t = \frac{15\ m}{45 \ m/s} \\\\t = 0.33 \ s](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bd%7D%7Bv%7D%20%5C%5C%5C%5Ct%20%3D%20%5Cfrac%7B15%5C%20m%7D%7B45%20%5C%20m%2Fs%7D%20%5C%5C%5C%5Ct%20%3D%200.33%20%5C%20s)
The distance traveled by the hockey player at the calculated time is;
![d = vt\\\\d = 0.075 \ m/s \ \times 0.33 \ s\\\\d = 0.025 \ m](https://tex.z-dn.net/?f=d%20%3D%20vt%5C%5C%5C%5Cd%20%3D%200.075%20%5C%20m%2Fs%20%5C%20%5Ctimes%200.33%20%5C%20s%5C%5C%5C%5Cd%20%3D%200.025%20%5C%20m)
Learn more about conservation of linear momentum here: brainly.com/question/7538238
Answer:
7.5 N/m
Explanation:
Potential energy of a spring can be calculated using below formula
Potential energy= 1/2kx^2
potential energy = 60 J
X= displacement = 4 m
K= spring constant=?
Substitute the values we have
60= 1/2 × K × 4^2
60= 1/2 × K × 16
60= K × 8
K= 7.5 N/m
Hence, the spring constant of the spring is 7.5 N/m
Answer:
The answer is below
Explanation:
Let a be the initial velocity of motorcycle A and b be the initial velocity of motorcycle B.
After 5.68 seconds, both motorcycle had the same velocity (v), therefore for motorcycle A:
(a - v) / 5.68 = 3.87
a - v = 21.9816
v = a - 21.9816
For motorcycle B:
(b - v) / 5.68 = 18.2
b - v = 103.376
v = b - 103.376
Therefore:
a - 21.9816 = b - 103.376
b - a = -21.9816 + 103.376
b - a = 81.3944
a) The difference between their speeds at the beginning was 81.3944 m/s
b) Since b - a = 81.3944. This means that the initial velocity of motorcycle B is greater than that of motorcycle A by 81.3944 m/s.
Therefore motorcycle B was moving faster