## Two identical masses are released from rest in a smooth hemispherical bowl of radius R from the positions shown. You can ignore friction between the

## Physics 221 Test #3 Fall 2021

262Phys_221C_Test_3_Fall_2021

1. Two identical masses are released from rest in a smooth hemispherical bowl of radius R from the positions shown. You can ignore friction between the masses and the surface of the bowl. If they stick together when they collide,

how high above the bottom of the bowl will the masses go after colliding?

[Express your final answer in terms of R.]

2. A uniform hollow rigid sphere of mass 1.000kg, initially at rest, is rolling down an incline making angle θ with the horizontal.

(circle the correct answer )

A) The acceleration of which point on the sphere is along the inclined plane?

(i) point o

(ii) any point on the sphere

(iii) point p

(iv) none of the above

B) The instantaneous axis of rotation [which is perpendicular to the page] passes through which point on the sphere?

(i) point p

(ii) any point on the sphere

(iii) point o

(iv) none of the above

C) Determine the acceleration of the center of mass of the sphere [first determine the angle of the incline from the geometry given in the figure].

D) What is the minimum coefficient of friction required to maintain pure rolling motion for the hollow sphere?

E) What is the c.m. kinetic energy of the sphere when the c.m falls by a distance h=0.4619m?

F) What is the rotational kinetic energy of the c.m. when the c.m falls by a distance h=0.4619m?

3.

4. Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 10.0 m/s toward the east and the other is traveling north with speed v2i. Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving

parallel skid marks at an angle of 55.0o north of east. [Ignore the external forces during collision].Let their final speed be v.

(a) What is the total momentum of the system right before and right after the collision in x direction in

terms of mass m of the automiboles?

Before: Ptot,x,i= After : Ptot,x,f= |

(b) What is the total momentum of the system right before and right after the collision in y direction in

terms of mass m of the automiboles?

Before: Ptot,y,i = After : Ptot,y,f= |

(c) The speed limit for both roads is 35 mi/h (=15.6 m/s) and the driver of the northwardmoving vehicle claims he was within the speed limit when the collision occurred. Is he

telling the truth?

(d) What is their final velocity

5. A 50.0-kg grindstone is a solid disk 0.260 m in radius. You press an ax down on the rim with a normal force of 160 N . The coefficient of kinetic friction between the blade and the stone is 0.60, and there is a constant friction torque of 6.5 Nm between the axle of the stone and its bearings.

A tangential force of magnitude F is applied at the end of a crank handle 0.5 m long to bring the stone from rest to 120 rev/min in 9.00 s.

(i) Determine the angular acceleration of the grindstone

(ii) Determine the net torque on the grindstone

(iii) Determine the torque exerted on the gride stone by the 160N force

(iv) Determine the friction force between the gride stone and the tip of the ax.

(v) Determine the torque exerted on the gride stone by the friction force.

(vi) Determine the magnitude of the force F that is applied at the end of a crank handle.

(vii) Determine the time it takes for the grindstone to come from 120 rev/min to rest if it is acted on by the axle friction alone. smooth hemispherical bowl

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