- #1
Telemachus
- 835
- 30
I need some help with the equation of moments for this exercise:
Each wheel of an automobile has a mass of 22 kg, a diameter of 575 mm, and a radius of gyration of 225 mm. The automobile travels around an unbanked curve of radius 150 m at a speed of 95 km/h. Knowing that the transverse distance between the wheels is 1.5 m, determine the additional normal force exerted by the ground on each outside wheel due to the motion of the car.
Well, at first I've computed the angular speed over the y and z axis and made this (horrible) draw.
[tex]w_y0.2875m=26.98\frac{m}{s}\rightarrow{w_y=92\frac{rad}{s}}[/tex]
[tex]w_z150m=26.98\frac{m}{s}\rightarrow{w_z=0.17\frac{rad}{s}}[/tex]
Now I must compute the moment equations, and the Newton equations.
[tex]N_1+N_2-mg=0[/tex]
[tex]Fr_1+Fr_2=m\displaystyle\frac{V^2}{\rho}[/tex]
Now I thought of taking moments at the origin of the system I draw at the picture. Would this be right?
And then:
[tex]M_x+N_1(150m+0.75m)+N_2(150m-0.75m)-mg150m=I_{xx}\dot\omega-I_{yz}w_z^2[/tex]
Where [tex]\dot\omega=w_z\times{w_y}[/tex]
Is this right? I can calculate the products of inertia, but I'm not sure about if what I'm doing is right, and then if I'm going to get [tex]M_x[/tex] with it.
Help please.
Each wheel of an automobile has a mass of 22 kg, a diameter of 575 mm, and a radius of gyration of 225 mm. The automobile travels around an unbanked curve of radius 150 m at a speed of 95 km/h. Knowing that the transverse distance between the wheels is 1.5 m, determine the additional normal force exerted by the ground on each outside wheel due to the motion of the car.
Well, at first I've computed the angular speed over the y and z axis and made this (horrible) draw.
[tex]w_y0.2875m=26.98\frac{m}{s}\rightarrow{w_y=92\frac{rad}{s}}[/tex]
[tex]w_z150m=26.98\frac{m}{s}\rightarrow{w_z=0.17\frac{rad}{s}}[/tex]
Now I must compute the moment equations, and the Newton equations.
[tex]N_1+N_2-mg=0[/tex]
[tex]Fr_1+Fr_2=m\displaystyle\frac{V^2}{\rho}[/tex]
Now I thought of taking moments at the origin of the system I draw at the picture. Would this be right?
And then:
[tex]M_x+N_1(150m+0.75m)+N_2(150m-0.75m)-mg150m=I_{xx}\dot\omega-I_{yz}w_z^2[/tex]
Where [tex]\dot\omega=w_z\times{w_y}[/tex]
Is this right? I can calculate the products of inertia, but I'm not sure about if what I'm doing is right, and then if I'm going to get [tex]M_x[/tex] with it.
Help please.
