A lever is used to lift a boulder. The fulcrum is placed 1.60 m away from the end at which you exert a downward force, producing a torque with a magnitude of 4.00 × 10^2 N • m. If the angle between the force and the lever is 80.0°, what is the magnitude of the applied force? Assume that the lever is massless.

A lever is used to lift a boulder. The fulcrum is placed 1.60 m away from the end at which you exert a downward force, producing a torque with a magnitude of 4.00 × 10^2 N • m. If the angle between the force and the lever is 80.0°, what is the magnitude of the applied force? Assume that the lever is massless.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 14OQ: A rod 7.0 m long is pivoted at a point 2.0 m from the left end. A downward force of 50 N acts at the...

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A rod 7.0 m long is pivoted at a point 2.0 m from the left end. A downward force of 50 N acts at the left end, and a downward force of 200 N acts at the right end. At what distance to the right of the pivot can a third force of 300 N acting upward be placed to produce rotational equilibrium? Note: Neglect the weight of the rod. (a) 1.0 m (b) 2.0 m (c) 3.0 m (d) 4.0 m (e) 3.5 m
As shown in Figure OQ10.9, a cord is wrapped onto a cylindrical reel mounted on a fixed, frictionless, horizontal axle. When does the reel have a greater magnitude of angular acceleration? (a) When the cord is pulled down with a constant force of 50 N. (b) When an object of weight 50 N is hung from the cord and released. (c) The angular accelerations in parts (a) and (b) are equal. (d) It is impossible to determine. Figure OQ10.9
A war-wolf, or trebuchet, is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport. A simple trebuchet is shown in Figure P10.19. Model it as a stiff rod of negligible mass, 3.00 m long, joining particles of mass m1 = 0.120 kg and m2 = 60.0 kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and 14.0 cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation. (a) Find the maximum speed that the small-mass object attains. (b) While the small-mass object is gaining speed, does it move with constant acceleration? (c) Does it move with constant tangential acceleration? (d) Does the trebuchet move with constant angular acceleration? (e) Does it have constant momentum? (f) Does the trebuchetEarth system have constant mechanical energy?
a small 0.171 kg block slides down a frictionless surface through height h = 0.893 m and then sticks to a uniform vertical rod of mass M = 0.342 kg and length d = 2.12 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ.
In the figure, a small 0.182 kg block slides down a frictionless surface through height h = 0.846 m and then sticks to a uniform vertical rod of mass M = 0.364 kg and length d = 1.92 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ
Given the magnitude of two vectors below and their dot product, what is the angle (in radians) between the two vectors? |A|=1.48 N |B|= 6.25 N |AxB|=8.0237 N^2
In the figure, two blocks, of masses 2.00 kg and 3.00 kg, are connected by a light string that passesover a frictionless pulley of moment of inertia 0.00400 kg · m2 and radius 5.00 cm. The coefficient offriction for the tabletop is 0.300. The blocks are released from rest. Using energy methods, find thespeed of the upper block just as it has moved 0.600 m. A) 3.19 m/s B) 1.40 m/s C) 1.22 m/s D) 1.95 m/s E) 5.44 m/s
Given the magnitude of two vectors below and their dot product, what is the angle (in radians) between the two vectors? |A|=4.55 N |B|=8.28N A.B= -20.935 N^2
A 4.00 m length of lightweight cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.28 kg. The spool is mounted on an axle with negligible friction and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 3.00 m/s2. (a)How much work has been done on the spool (in J) when it reaches an angular speed of 5.47 rad/s? (b)How long (in s) does it take the spool to reach this angular speed? (c)How much cord is left on the spool (in m) when it reaches this angular speed?
A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. If the cylinder has a mass of 10 kg, what is its linear kinetic energy? a. 0 J b. 121.6 J c. 41.6 J d. 80 J
In the figure, a small block of mass m = 0.037 kg can slide along the frictionless loop-the-loop, with loop radius R = 17 cm. The block is released from rest at point P, at height h = 5R above the bottom of the loop. What are the magnitudes of (a) the horizontal component and (b) the vertical component of the net force acting on the block at point Q? (c) At what height h should the block be released from rest so that it is on the verge of losing contact with the track at the top of the loop? (On the verge of losing contact means that the normal force on the block from the track has just then become zero).
A hanging weight, with a mass of m1 = 0.370 kg, is attached by a string to a block with mass m2 = 0.820 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R1 = 0.0200 m, and an outer radius of R2 = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is ?k = 0.250. At the instant shown, the block is moving with a velocity of vi = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible. (a)Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. (b)What is the angular speed of the pulley (in rad/s) after the block has moved this distance?