Free Body Diagram Exercises

Transcription

1 Free ody iagram xercises

2 F- 1 xample: Free ody iagrams The roller-band device consists of two rollers, each of radius, r, encircled by a flexible band of negligible thickness and subjected to the two tensions T. raw the F to allow the contact force, R, between the band and the flat supporting surfaces at and to be determined. The action is in the horizontal plane (i.e., plan view), so that the weights of the rollers and band are not involved. T r r T

3 F- 2 xample: Free ody iagrams etermine the tensions in all ropes in the pulley system below. Pulley is attached at the wall but the other pulleys are suspended. The weights of the pulleys are small compared to the load. raw the F. T 500 kg

4 F- 3 xample: Free ody iagrams uniform pole of mass m is being hoisted into position by a winch. The horizontal supporting surface is notched at the pole support. What s wrong with the F? F T mg Notch R Is the pole in equilibrium?

5 F- 4 xample: Free ody iagrams onstruct the F for the transit which has a weight of 90 N. a. Ignore the weight of the legs. b. Include the weight of the legs. y 1.2 m 0.60 m x 0.60 m 0.60 m z 0.45 m

6 F- 5 xample: Free ody iagrams The 200 kg T-frame has its center of mass at G. alculate the total force supported by the pin at O after the 3 kn force is applied to the cable. raw the F. 3 kn 2.5 m 2.5 m O 2 m G 30 o 4 m 2.5 m 2.5 m O 2 m G 4 m

7 F- 6 xample: Free ody iagrams The welded tubular frame is secured to the horizontal x-z plane by a ball-and-socket joint at and receives support from the loose fitting ring at. Under the action of the 2-kN load, rotation about a line from to is prevented by the cable, and the frame is stable. Neglect the weight of the frame. raw the F. y y 2 kn 2 kn z x z x

8 F- 7 xample: Free ody iagrams The bent bar of negligible weight is supported by a ball-and-socket joint at O, a cable connected between and, and a slider bearing at. The bar is acted on by a vertical down force P at and a couple parallel to the y-axis. raw the F. y z O x O P

9 F- 8 xample: Free ody iagrams ars and are both connected to walls with ball-and-socket connections. raw the F assuming the weights of the bars to be negligible and then draw the F assuming the weights of the bars are significant. y 2 m 2 m z 3 m 3 m 4 m x 3 m Weights are negligible: y 2 m z 2 m 3 m 3 m x 3 m 4 m y z x Weights are significant: 2 m z y 2 m 3 m 3 m x 3 m 4 m y z x

10 F- 9 xample: Free ody iagrams Wheel of mass m on verge of being pulled over the curb by the force P. raw the F. P

11 F- 10 xample: Free ody iagrams The uniform rod is supported by a ball-and-socket joint at and leans against both the rod and the vertical wall. ll surfaces are frictionless. etermine the reactions at and. raw the F. y x z

12 F- 11 xample: Free ody iagrams The structure below is loaded by a couple M applied to member. Neglecting the weight of the members, determine all forces acting on the structure. cable is connected at. raw the F. M

13 F- 12 xample: Free ody iagrams piston is used to crush a can, by applying a force P to the lever. onnections at,, and are frictionless pins. Ignore the mass of all components. etermine the reactions at and. raw the F. P

14 F- 13 xample: Free ody iagrams force P (that has x, y, and z components) is applied to the handle of the hoist. The bearing supports the thrust (force in the direction of the shaft axis), while bearing supports only radial load (load normal to the shaft axis). raw the F to determine the mass m that can be supported and the total radial force exerted on the shaft by each bearing. ssume neither bearing to be capable of supporting a moment about a line normal to the shaft axis. raw Fs for the x-y, x-z, and z-x planes. y m z x P

15 F- 14 xample: Free ody iagrams The smooth disk is pinned at and has a weight of W. Neglecting the weights of the other members, draw the Fs of the components of the assembly. W

16 F- 15 xample: Free ody iagrams The folding chair sitting on the lawn is loaded as shown. The weights of the members are negligible. raw the F. P F G H I J P F F G G H H I I J

17 F- 16 xample: Free ody iagrams alculate the forces acting at and for the frame loaded by the couple M. Ignore the weight of the members. raw the F. M

18 F- 17 xample: Free ody iagrams The machine shown is designed as an overload protection device which releases the load when it exceeds a predetermined value T. soft metal shear pin at G is inserted into a hole in the lower half and is acted on by the upper half. When the total force on the pin exceeds its strength, it will break. The two halves then rotate about F under the tensions in and as shown in the second diagram. raw the F to allow one to determine the maximum allowable tension, T given the maximum force that the shear pin will bear. T G F T Released position

19 F- 18 xample: Free ody iagrams The hydraulic truck-mounted crane shown below is used to lift a beam that has a mass M. raw the Fs of each of its members and separate Fs of the pins at and. F G H I F F G G H H I W

20 F- 19 xample: Free ody iagrams The bar is pinned into each support at and subjected to the force P and couple M. The supports at prevent axial movement. raw the F. M P

21 F- 20 xample: Free ody iagrams backhoe boom and bucket with a load W acting at G is shown. raw the Fs of the components. F G H H I F G H I

22 F- 21 xample: Free ody iagrams raw the F to determine the banking angle θ for the race track so that the wheels of the racing car will not have to depend upon friction to prevent the car from sliding laterally. ssume the cars have a negligible size, a mass m and travel around the curve of radius ρ with a speed, v. θ