2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 1

The arm OA of the classifying accelerometer has mass of 0.25 kg with center of mass at G. The adjusting screw and spring are preset to a force of 12 N at B. At what acceleration a would the electrical contacts at A be on the verge of opening? Motion is in the vertical plane of the figure.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 2

The homogeneous crate of mass m is mounted on small wheels as shown. Determine the maximum force P which can be applied without overturning the crate about (a) its lower front edge with h = b and (b) its lower back edge with h = 0.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 3

Determine the vale of the force P which would cause the cabinet to begin to tip. What coefficient sμ of static friction is necessary to ensure that tipping occurs without slipping?

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 4

The vertical bar AB has a mass of 150 kg with center of mass G midway between the ends. The bar is elevated from rest at 0θ = by means of the parallel links of negligible mass, with a constant couple M = 5 kN⋅m applied to the lower link at C. Determine the angular acceleration α of the links as a function of θ and find the force B in the link DB at the instant when 30θ = ° .

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 5

Each of the two drums and connected hubs of 250-mm radius has a mass of 100 kg and has a radius of gyration about its center of 375 mm. Calculate the angular acceleration of each drum. Friction in each bearing is negligible.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 6

The pendulum has a mass of 7.5 kg with center of mass G and has a radius of gyration about the pivot O of 295 mm. If the pendulum is released from rest at 0θ = , determine the total force supported by the bearing at the instant when 60θ = ° . Friction in the bearing is negligible.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 7

The solid cylindrical rotor B has a mass of 43 kg and is mounted on its central axis C-C. The frame A rotates about the fixed vertical axis O-O under the applied torque M = 30 Nm. The rotor may be unlocked from the frame by withdrawing the locking pin P. Calculate the angular acceleration α of the frame A if the locking pin is (a) in place and (b) withdrawn. Neglect all friction and the mass of the frame.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 8

The solid homogeneous cylinder is released from rest on the ramp. If 40θ = ° , 0.30sμ = and

0.20kμ = , determine the acceleration of the mass center G and the friction force exerted by the ramp on the cylinder. Repeat the problem with the following conditions: 30θ = ° , 0.15sμ = and

0.10kμ = .

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 9

The slender rod of mass m and length l is released from rest in the vertical position with the roller at end A resting on the incline. Determine the initial acceleration of A.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 10

A 6.4-kg bowling ball with a circumference of 690 mm has a radius of gyration of 83 mm. If the ball is released with a velocity of 6 m/s but with no angular velocity as it touches the alley floor, compute the distance traveled by the ball before it begins to roll without slipping. The coefficient of friction between the ball and the floor is 0.20.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Force-mass-acceleration: Example 11

The small end rollers of the 3.6-kg uniform slender bar are constrained to move in the slots, which lie in a vertical plane. At the instant when 30θ = ° , the angular velocity of the bar is 2 rad/s counter-clockwise. Determine the angular acceleration of the bar, the reactions at A and B, and the accelerations of points A and B under the action of the 26-N force P. Neglect the friction and mass of the small rollers.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Work and energy: Example 1

The velocity of the 8-kg cylinder is 0.3m/s at a certain instant. What is its speed v after dropping an additional 1.5 m? The mass of the grooved drum is 12 kg, its centroidal radius of gyration is 210k = mm, and the radius of its groove is 200ir = mm. The frictional moment at O is a constant 3 Nm.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Work and energy: Example 2

The wheel rolls up the incline on its hubs without slipping and is pulled by the 100-N force applied to the cord wrapped around its outer rim. If the wheel starts from rest, compute its angular velocity ω after its center has moved a distance of 3 m up the incline. The wheel has a mass of 40 kg with center of mass at O and has a centroidal radius of gyration of 150 mm. Determine the power input from the 100-N force at the end of the 3-m motion interval.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Work and energy: Example 3

In the mechanism shown, each of the two wheels has a mass of 30 kg and a centroidal radius of gyration of 100 mm. Each link OB has a mass of 10 kg and may be treated as a slender bar. The 7-kg collar at B slides on the fixed vertical shaft with negligible friction. The spring has a stiffness k = 30 kN/m and is contacted by the bottom of the collar when the links reach the horizontal position. If the collar is released from rest at the position 45θ = ° and if friction is sufficient to prevent the wheels from slipping, determine (a) the velocity vB of the collar as it first strikes the spring and (b) the maximum deformation x of the spring.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Work and energy: Example 4

The two slender bars each of mass m and length b are pinned together and move in the vertical plane. If the bars are released from rest in the position shown and move together under the action of a couple M of constant magnitude applied to AB, determine the velocity of A as it strikes O.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Impulse and momentum: Example 1

The force P, which is applied to the cable wrapped around the central hub of the symmetrical wheel, is increased slowly according to P = 6.5t, where P is in newtons and t is the time in seconds after P is first applied. Determine the angular velocity 2ω of the wheel 10 seconds after P is applied if the

wheel is rolling to the left with a velocity of its center of 0.9 m/s at time t = 0. The wheel, which has a mass of 60 kg and a radius of gyration about its center of 250 mm, rolls without slipping.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Impulse and momentum: Example 2

The sheave E of the hoisting rig shown has a mass of 30 kg and a centroidal radius of gyration of 250 mm. The 40-kg load D which is carried by the sheave has an initial downward velocity 1 1.2v = m/s at

the instant when a clockwise torque is applied to the hoisting drum A to maintain essentially a constant force F = 380 N in the cable B. Compute the angular velocity 2ω of the heave 5 seconds after

the torque is applied to the drum and find the tension T in the cable at O during the interval. Neglect all friction.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Impulse and momentum: Example 3

Determine the minimum velocity v which the wheel must have to just roll over the obstruction. The centroidal radius of gyration of the wheel is k, and it is assumed that the wheel does not slip.

2103-212 Dynamics Kinetics of rigid bodies Section 4: TJW Impulse and momentum: Example 4

The 30-kg wheel has a radius of gyration about its center of 75 mm and is rotating clockwise at the rate of 300 rpm when it is released onto the incline with no velocity of its center O. While the wheel is slipping, it is observed that the center O remains in a fixed position. Determine the coefficient of kinetic friction kμ and the time t during which slipping occurs. Also determine the velocity v of the

center 4 seconds after the wheel has stopped slipping.