Respuesta :
Answer:
mass of clay = 8 kg
Explanation:
Rotational inertia of wheel = [tex]I_{w}=46kg.m^{2}[/tex]
Angular speed of wheel =ω₁ = 40 rpm = 4.188 rad/sec
Clay drops on wheel from distance = r= 1.2 m
Angular speed of clay and wheel = ω₂ = 32 rpm = 3.35 rad/sec
To find:
Mass of clay = M =?
Angular momentum before clay drop = [tex]L_{1}=I_{w} \omega[/tex]
[tex]L_{1}=(46)(4.188)[/tex]
[tex]L_{1}=192.648kg.m^{2}/sec[/tex]
After collision, angular momentum = [tex]L_{2}=I_{c+w} \omega_{2}[/tex]
Using concept of conservation of angular momentum
L₁ = L₂
[tex]192.648=I_{c+w} \omega_{2}[/tex]
[tex]I_{c+w} =\farc{192.648}{3.35}[/tex]
[tex]I_{c+w} =\farc{192.648}{3.35}[/tex]
[tex]I_{c+w} =57.50 kg.m^{2}[/tex]
[tex]I_{c+w} = I_{c}+I_{w}[/tex]
[tex] I_{c}=I_{c+w}-I_{w}[/tex]
[tex] I_{c}=57.50-46[/tex]
[tex] I_{c}=11.50[/tex]
[tex] I_{c}=m.r^{2}[/tex]
[tex]m=\frac{I_{c}}{r^{2}}[/tex]
[tex]m=8 kg[/tex]
The angular momentum of the body before the collision is always equal to the angular momentum of the body after the collision. The mass of the clay will be 8 kg.
What is the law of conservation of angular momentum?
According to the law of conservation of angular momentum, the angular momentum of the body before the collision is always equal to the angular momentum of the body after the collision.
The angular momentum of the body is given by the product of the mass and velocity of the body.
Angular momentum before clay drop = L₁= Iω = 46×4.188= 192.648 kgm²/sec.
The given data in the problem is ;
I is the rotational inertia of wheel =
ω₁ is the angular speed of wheel= 40 rpm = 4.188 rad/sec
r is the distance from the clay drops on the wheel 1.2 m
ω₂ is the angular speed of clay and wheel = 32 rpm = 3.35 rad/sec
M is the mass of clay=?
According to the law of conservation of angular momentum
Angular Momentum before clay drop =Momentum after clay drop
[tex]\rm L_1= L_2 \\\\ 192.648 = I_{C+\omega} \omega_2 \\\\ I_{C+\omega} =192.6483 \\\\ I_{C+\omega}=57.50 Kgm^2 \\\\ I_{C+\omega} = I_C+ I_\omega \\\\ I_c= i{c+ \omega}- I_{\omega} \\\\ I_c = 57.50 -4.6 \\\\ I_c= 11.50 \\\\ I_C= mr^2 \\\\ m = 8 Kg[/tex]
Hence the mass of the clay will be 8 kg.
To learn more about the angular momentum refer to the link;
https://brainly.com/question/1113396
