Don't use chat gpt It 1) A solid cylinder with radius r and mass m has a massless cord wrapped around it and is allowedto drop.(i) Draw a free-body diagram with all forces and lever arms.(iii) What is the tension T in the cord in terms of mg?T(ii) What is the acceleration a of the cylinder in terms of g?T =(iv) If the cylinder bounces elastically at the end of the cord and rolls back up the string, what isthe tension T in the string as it rises?a =T=

Answered: 1) A solid cylinder with radius r and…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter5: Displacement And Force In Two Dimensions

Section: Chapter Questions

Problem 82A

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To get up on the roof, a person (mass 70.0 kg) places 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to frictionless. The center of ladder is 2.00 m from the bottom. The person is standing 3.00 m from the bottom. Find the normal reaction and friction forces on the ladder at its base.
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?
Figure P12.67 shows a vertical force applied tangentially to a uniform cylinder of weight Fg. The coefficient of static friction between the cylinder and all surfaces is 0.500. The force P is increased in magnitude until the cylinder begins to rotate. In terms of Fg find the maximum force magnitude P that can be applied without causing the cylinder to rotate. Suggestion: Show that both friction forces will be at their maximum values when the cylinder is on the verge of slipping.
Figure CQ10.15 shows a side view of a childs tricycle with rubber tires on a horizontal concrete sidewalk. If a string were attached to the upper pedal on the far side and pulled forward horizontally, the tricycle would start to roll forward. (a) Instead, assume a siring is attached to the lower pedal on the near side and pulled forward horizontally as shown by A. Will the tricycle start to roll? If so, which way? Answer the same questions if (b) the string is pulled forward and upward as shown by B, (c) if the string is pulled straight down as shown by C, and (d) if the string is pulled forward and downward as shown by D. (e) What If? Suppose the string is instead attached to the rim of the front wheel and pulled upward and backward as shown by E. Which way does the tricycle roll? (f) Explain a pattern of reasoning, based on the figure, that makes it easy to answer questions such as these. What physical quantity must you evaluate? Figure CQ10.15
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.)
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?
A diver off the high board imparts an initial rotation with his body fully extended before going into a tuck and executing three back somersaults before hitting the water. If his moment of inertia before the tuck is 16.9kgm2 and after the tuck during the somersaults is 4.2kgm2 , what rotation rate must he impart to his body directly off the board and before the tuck if he takes 1.4 s to execute the somersaults before hitting the water?
Jamal and Dayo are lifting a large chest, weighing 207 lb, by using the two rope handles attached to either side. As they lift and hold it up so that it is motionless, each handle makes a different angle with respect to the vertical side of the chest (Fig. P5.76). If the angle between Jamals handle and the vertical side is 25.0 and the angle between Dayos handle and the vertical side of the chest is 30.0, what are the tensions in each handle? FIGURE P5.76
If you were to stop a spinning wheel with a constant force, where on the wheel would you apply the force to produce the maximum negative acceleration?
A bowling ball of radius 8.5 cm is tossed onto a bowling lane with speed 9.0 m/s. The direction of the toss is to the left, as viewed by the observer, so the bowing ball starts to rotate counterclockwise when in contact with the floor. The coefficient of kinetic friction on the lane is 0.3. (a) What is the time required for the ball to come to the point where It is no slipping? What is the distance d to the point where the ball is rolling without slipping?
Section 11.5 The Motion of Gyroscopes and Tops A spacecraft is in empty space. It carries on board gyroscope with a moment of inertia of Ig = 20.0 kgm2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is Is = 5.00 X 105 kgm2. Neither the spacecraft nor the gyroscope is originally rotating. The gyroscope can be powered up in a negligible period of time to an angular speed of 100 rad/s. If the orientation of the spacecraft is to be changed by 30.0, for what time interval should the gyroscope be operated?
Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen below. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the centripetal force) and the vertical normal force (which must equal the system’s weight). (a) Show that (as defined as shown) is related to the speed vand radius of curvature rof the turn in the same way as for an ideally banked roadway—that is, =tan1(v2/rg) . (b) Calculate for a 12.0-m/s turn of radius 30.0 m (as in a race).

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