PROBLEM 2 A cube of mass m is placed in a rotating funnel. (The funnel is rotating around the vertical axis shown in the diagram.) There is no friction between the cube and the funnel but the funnel is rotating at just the right speed needed to keep the cube rotating with the funnel. The cube travels in a circular path of radius r, and the angle between the vertical and the wall of the funnel is 0. Express your answers to parts (b) and (c) in terms of m, r, g, and/or 0. (a) Sketch a free-body diagram for the cube. Show all the forces acting on it, and show the appropriate coordinate system to use for this problem. (b) What is the normal force acting on the cube? FN=mg58 (c) What is the speed v of the cube? (d) If the speed of the cube is different from what you determined in part (c), a force of friction is necessary to keep the cube from slipping in the funnel. If the funnel is rotating slower than it was above, draw a new free-body diagram for the cube to show which way friction acts. Assume the cube rotates with the funnel without slipping, and indicate on your diagram whether the force of friction is static (Fs) or kinetic (Fk). FN= v=

PROBLEM 2 A cube of mass m is placed in a rotating funnel. (The funnel is rotating around the vertical axis shown in the diagram.) There is no friction between the cube and the funnel but the funnel is rotating at just the right speed needed to keep the cube rotating with the funnel. The cube travels in a circular path of radius r, and the angle between the vertical and the wall of the funnel is 0. Express your answers to parts (b) and (c) in terms of m, r, g, and/or 0. (a) Sketch a free-body diagram for the cube. Show all the forces acting on it, and show the appropriate coordinate system to use for this problem. (b) What is the normal force acting on the cube? FN=mg58 (c) What is the speed v of the cube? (d) If the speed of the cube is different from what you determined in part (c), a force of friction is necessary to keep the cube from slipping in the funnel. If the funnel is rotating slower than it was above, draw a new free-body diagram for the cube to show which way friction acts. Assume the cube rotates with the funnel without slipping, and indicate on your diagram whether the force of friction is static (Fs) or kinetic (Fk). FN= v=

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter2: Motion

Section2.3: Acceleration

Problem 2.3CE: What is the average speed in mi/h of a person at the equator as a result of the Earths rotation?...

See similar textbooks

Similar questions

Keratinocytes are the most common cells in the skins outer layer. As these approximately circular cells migrate across a wound during the healing process, they roll in a way that reduces the frictional forces impeding their motion. (a) Given a cell body diameter of 1.00 105 m (10 m), what minimum angular speed would be required to produce the observed linear speed of 1.67 107 m/s (10 m/min)? (b) How many complete revolutions would be required for the cell to roll a distance of 5.00 103 m? (Because of slipping as the cells roll, averages of observed angular speeds and the number of complete revolutions are about three times these minimum values.)
A space station, in the form of a wheel 120 m in diameter, rotates to provide an artificial gravity of 3.00 m/s2 for persons who walk around on the inner wall of the outer rim. Find the rate of the wheels rotation in revolutions per minute that will produce this effect.
A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with respect to each other. The masses and distances to the axis of the point particles are m1=0.1kg , r1=0.2m , m2=0.05kg , r2=0.4m , m3=0.5kg , r3=0.01m . (a) What is the moment of inertia of the system? (b) What is the rotational kinetic energy of the system?
Suppose when Earth was created, it was not rotating. However, after the application of a uniform torque after 6 days, it was rotating at 1 rev/day. (a) What was the angular acceleration during the 6 days? (b) What torque was applied to Earth during this period? (c) What force tangent to Earth at its equator would produce this torque?
You have a grindstone (a disk) that is 90.0 kg, has a 0.340-m radius, and is turning at 90.0 rpm, and you press a steel axe against it with a radial force of 20.0 N. (a) Assuming the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstine. (b) How many turns will the stone make before coming to rest?
A point on a rotating turntable 20.0 cm from the center accelerates from rest to a final speed of 0.700 m/s in 1.75 s. At t = 1.25 s, find the magnitude and direction of (a) the radial acceleration, (b) the tangential acceleration, and (c) the total acceleration of the point.
The angular acceleration of a rotating rigid body is given by =(2.0-3.0t)rad/s2 . If the body starts rotating from rest at t=0 , (a) what is the angular velocity? (b) Angular position? (c) What angle does it rotate through in 10 s? (d) Where does the vector perpendicular to the axis of rotation indicating 0 at t=0 lie at t=10s ?
A torque of 50.0Nm is applied to a grinding wheel (l=20.0kgm2) for 20 s. (a) If it starts from rest, what is the angular velocity of the grinding wheel after the troque is removed? (b) Through what angle does the wheel move while the torque is applied?
The centrifuge at NASA Ames Research Center has a radius of 8.8 m and can produce farces on its payload of 20 gs or 20 times the force of gravity on Earth. (a) What is the angular momentum of a 20-kg payload that experiences 10 gs in the centrifuge? (b) If the driver motor was turned off in (a) and the payload lost 10 kg, what would be its new spin rate, taking into account there are no frictional forces present?
An ultracentrifuge accelerates from to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s2 ? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the centripetal acceleration in m/s2 and multiples of g of this point at full rpm? (d) What is the total distance travelled by a point 9.5 cm from the axis of totation of the ultracentrifuge?
A particle moves 3.0 m along a circle of radius 1.5 m. (a) Through what angle does it rotate? (b) If the particle makes this trip in 1.0 s at a constant speed, what is its angular velocity? (c) What is its acceleration?
In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for the rockets position measured from the center of the Earth is given by y(t)=(R3/2+3g2Rt)2/3j where R is the radius of the Earth (6.38 106 m) and g is the constant acceleration of an object in free fall near the Earths surface (9.81 m/s2). a. Derive expressions for vy(t) and ay(t). b. Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful.) c. When will the rocket be at y=4R? d. What are vy and ay when y=4R?