A hollow, spherical shell with mass 4.00kg rolls without slipping down a 37.0° s

Question

A hollow, spherical shell with mass 4.00kg rolls without slipping down a 37.0° slope. (a) Find the acceleration.
1 m/s2
Find the friction force.
2 N
Find the minimum coefficient of friction needed to preventslipping.
3

(b) How would your answers to part (a) change if the mass weredoubled to 8.00 kg?
Acceleration
4 m/s2
Friction force
5 N
Coefficient of friction
6 (a) Find the acceleration.
1 m/s2
Find the friction force.
2 N
Find the minimum coefficient of friction needed to preventslipping.
3

(b) How would your answers to part (a) change if the mass weredoubled to 8.00 kg?
Acceleration
4 m/s2
Friction force
5 N
Coefficient of friction
6

Explanation / Answer

(a) torque = static friction force * R = I .              F R = (2/3) M R2 (a/R) . Also...    mg sin - F = M a   .                         F = (2/3) M a .            Mg sin - (2/3) Ma = Ma .            gsin = (5/3) a .    a = 0.6 g sin = 0.6 * 9.80 * sin37 =   3.539m/s2 . Fromabove... F = (2/3) M a = (2/3)* 4.00 * 3.539   = 9.437Newtons . Minimum coeff of friction is foundby... .         friction force = coeff * normalforce .         F = u * mg cos37 .     u  = F / mg cos 37 = 9.437 / 4.00 * 9.80 *cos37 =    0.301 . (b)   If the mass was doubledto 8.00 kg, .     the accelerationwould still be the same       =   3.539m/s2 . The friction force would double (noticethat we used the mass in this calculation)to:    18.874 N . the minimum coeff of frictionwould stay the same   (notice we divided back again bythe mass)    0.301 . Fromabove... F = (2/3) M a = (2/3)* 4.00 * 3.539   = 9.437Newtons . Minimum coeff of friction is foundby... .         friction force = coeff * normalforce .         F = u * mg cos37 .     u  = F / mg cos 37 = 9.437 / 4.00 * 9.80 *cos37 =    0.301 . (b)   If the mass was doubledto 8.00 kg, .     the accelerationwould still be the same       =   3.539m/s2 . The friction force would double (noticethat we used the mass in this calculation)to:    18.874 N . the minimum coeff of frictionwould stay the same   (notice we divided back again bythe mass)    0.301 (b)   If the mass was doubledto 8.00 kg, .     the accelerationwould still be the same       =   3.539m/s2 . The friction force would double (noticethat we used the mass in this calculation)to:    18.874 N . the minimum coeff of frictionwould stay the same   (notice we divided back again bythe mass)    0.301 . The friction force would double (noticethat we used the mass in this calculation)to:    18.874 N . the minimum coeff of frictionwould stay the same   (notice we divided back again bythe mass)    0.301

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