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Parallel Forces Problems

(Online Source of Additional Problems at end of problems list. Also, check out the link to Cornell’s Physics Department located at the end of Set 2 problems, and the link to the University of Cincinnati at the end of Set 1 problems)

Set 1: Levers

Note:  Solutions or hints can be accessed by clicking on hyperlinked problem numbers.

1.      The steering wheel of a car is 7 dm in diameter and it turns a shaft 8 mm in diameter.  If a 90 Nt  force is needed to turn the wheel: 

        (A)  What torque will be exerted on the shaft? 

        (B)   What force is exerted tangentially to the shaft? 

 

2.     You must exert a force of 50-lbs in order to support a load of cement in a wheelbarrow.  Your hands on the handles are 4 ft from the axle of the wheel while the load in the wheelbarrow weighs 150-lb.  How far is the center of gravity of the cement from the axle? 

 

3.     A 20 cm diameter wheel and axle has a crank attached so that the handle is flush with the edge of the wheel.  The axle that runs through the center of the wheel has a diameter of 3.2 cm

        (A)  What force must be applied to the handle to just support a 10 Nt weight suspended from a cable attached to the axle? 

        (B)   What torque is produced by this force? 

 

3.      The shaft of a wheelbarrow is 6 dm long.  A 100 Nt box is placed at an average distance of 2 dm from the axle of the wheel.  What force must you exert to the handles to support the load?  (ans:  FE = 33.33 Nt)

 

4.      Another 100 Nt box is placed in the wheelbarrow of problem #3, at an average distance of 1 dm from the axle.  What force would you now need to exert to support the load?   (ans:  FE = 50 Nt)

 

5.      A man uses a 5 m bar to lift a 540 Nt object.  If the man pivots the bar 6 cm from the load, what force must he exert to support the load?  

6.      An 80 Nt boy sits at a distance of 4 dm from the fulcrum of a seesaw and just balances another boy who is sitting 5 dm on the other side of the pivot.  How much does the second boy weigh?   (ans:  64 Nt)

7.      A man lifts 1.5 x 106 dynes of coal in a shovel.  His left hand grasps the shovel at a distance of 30 cm from the end of the handle.  The center of gravity of the coal is 20 cm from the left hand and his right hand grasps the end of the handle.

        (A)  What force must be applied by his right hand? 

        (B)   What force must be exerted by his left hand? 

 

8.      A uniform bar 180 cm weighs 9 Nt.  The bar is pivoted at a point 15 cm from the middle. Where should a 7 Nt weight be attached to balance the bar?    (ans:  19 cm from pivot) 

9.      A baseball bat 3.6 dm long is pivoted at its geometric center and balances when a 0.5 Nt weight is attached to the end of the handle.  If the bat weighs 2 Nt, where is the bat’s center of gravity?  

10.    A pole 2.5 m in length weighs 180Nt and IS NOT of uniform construction.  If, when the pole is lying on the ground, a force of 100 Nt is required to raise the thick end, where is the center of gravity of the pole?    

11.    A uniform bar1meter in length weighs 400 Nt and is pivoted at the 40 cm point. We suspend a 20 Nt weight at the 5 cm point and a 30 Nt weight at the 70 cm point.  Where must we place a 210 Nt weight to balance the bar?  (ans:  20 cm to left of pivot, or on the 20 cm mark)

12.    A construction worker uses a wheelbarrow whose handles are 9 ft in length and weighs 8-lbs to transport several rocks.  The rocks are distributed as follows:  a 20-lb rock is 2 ft from the axle, a 35-lb rock is 1 ft from the 20-lb rock, and a 26-lb rock is located 3 ft from the 20-lb rock.  What force must the worker exert on the handles to support the load?  

13.    A pole 6 m in length is used as a second class lever to lift a 600 kg mass.  Where must the load be located if the maximum force that you have available to support the load is 750 Nt?   (ans:  0.77 m from pivot)

14.    A plank 1.6 m in length is used as a lever to support a 1200 Nt load.

        (A)   Where must the pivot be located if the maximum force that you have available to support the load is

                130 Nt?    

        (B)   What class lever(s) may be used?   (ans:  0.156 m from load if 1st class lever, 0.173 m from load if

                2nd class lever)

 

15.    A bar 2.5 m long is used as a second class lever to support a 50 kg load.  Where must the load be located if the largest force you have available is 39.2 Nt?   (ans:  0.2 m from pivot end) 

16.    A 5 kg mass is supported by a third class lever.  Where should a force of 215.6 Nt be applied to support the load if the lever is 100 cm in length?   (ans:  0.23 m)

17.    A workman must choose a wheelbarrow most appropriate for lifting a 220-lb load.  If he has been advised not to lift more than 60-lb, and he wants to place the load 18 in from the axle, what length wheelbarrow (from axle to end of handles) must he choose? 

18.   The MOMENT ARM of a 125-lb tension force,“FT”, acting on the horizontal bar with an angle of 30º, is:

            

19.    A motor, rated to pull no more than 500-lb resistance, is attached by a cable wrapped around the outer wheel (39.5 in diameter) of a dual pulley.  A 1200-lb crate is attached by another cable wrapped around a smaller adjacent wheel (18.0 in diameter) of the pulley system.  What resistance will the motor experience, and will it lift the crate?

          

      If the same motor and load are to be attached to a new wheel and axle device being manufactured, where the diameter of the outer wheel is 36 inches, what is the maximum allowed DIAMETER of the axle (or inner wheel)?

For a discussion on a biophysical problem involving torque related to the human arm, which is acting as a lever, go to the University of Cincinnati, Raymond Walters College “College Physics for Students of Chemistry and Biology.

 

 

 

 

  

 

Set 2: Distributed Loads:

Go to Set 2 Solutions 

20.  Four construction trucks are on a 245 ton bridge 350 ft in length.  The first truck weighs 12 tons and is 15 ft from the left end, the second truck weighs 10 tons and is 10 ft from the first truck, the third truck weighs 18 tons and is 60 ft from the second truck, and the fourth truck weighs 25 tons and is 5 ft from the right end of the bridge.  What force must EACH end of the bridge exert to support the load.

 

21.  Five painters stand on a 22.8 m long plank that is supported horizontally by a ladder at each end.  Each       painter has a mass of 75 kg , with the first painter located 1 m from one end and each painter thereafter            is 3 m from the one working next to him.  What force must EACH ladder exert to support this load?  

 

22. A 4 ton bridge 40 ft in length and of uniform construction supports 5 trucks.  The trucks weigh 1.5 tons, 4 tons, 2 tons, 10 tons, and 8 tons.  They are positioned on the bridge so that the first is 15 ft from one end and each truck is spaced so that their centers of gravity are 5 ft apart.  What force must EACH end    of the bridge exert to support this load?

 

23. A plank is supported horizontally by two ropes, one at each and.  The rope on the left end makes an angle of 50º with the bar while the one on the right end makes an angle of 40º with the bar.  The 12 ft plank is of uniform construction and weighs 25 lbs.  A 150-lb man stands 4 ft from the left end, a 160-lb man stands in the center, while a third man weighing 175-lb stands 3 ft from the right end.  What is the tension in each of the supporting ropes?

 

24.  Two men are carrying four buckets of water on a uniform 10 ft bar.  The bar weighs 10-lbs and the buckets  are as follows:  the first    bucket weighing 5-lbs is 2 ft from one end, the second is 1 ft from the first and weights 6-lbs, the third is 4 ft from the second and weighs 8-lbs, and the fourth is 1 ft from the third and weighs 10-lbs.  What force must EACH man exert to support the total load?

24.    A 25,000 Nt truck is located 20 m from one end of a 100 m bridge.  What part of the truck’s weight does EACH end support?

 

25.    A uniform bridge weighing 5 tons is 30 ft in length.  The bridge supports five trucks whose centers of gravity are 4 ft apart.  The first truck is 1 ft from the left end weighs 6 tons and each one thereafter weighs 2 tons, 4 tons, 8tons, and 10 tons, respectively.  What force must each end of the bridge exert to support this load?    

 

26.    What force does each support pillar exert to support the load indicated below?

               

 Demonstration, Carpenter on a plank Cornell University animation of an FA-FB problem.

 

Set 3: FX-DX, Extended Plank, Ladder, Storefront Sign:

Go to Set 3 Solutions (.doc) (.htm)

Go to Test 2 Review

27.    A 25 m long gangplank of uniform construction weighs 200 Nt.  It is resting on the end of a pier so that 5 m of its length extends out over the water.  A 190 Nt man walks out on the plank and stands at the end over the water.

(A)      Will he cause the plank to tip?

 Now suppose a 175  Nt man walks out on the plank to join the first man.

(B)       How far out may he walk without tipping the plank?

 

28.    A uniform 10 ft bar weighs 250-lbs.  The bar is placed so that 2 ft of its length extends out over the edge of the support.  How far out on the extended portion of the bar can a 300-lb box be placed to just balance the system?

29.    What weight must be used (FX) and where must it be placed (DX) if it is to produce total equilibrium in the following system:

                

30.    You are at a pool party where a 36 ft uniform 420-lb plank is placed so that 7 ft of its length extends out over the edge of a swimming pool.  A 180-lb person is standing on the end of the plank out over the water.  If you weigh 195-lb, would you be able to walk out and stand next to the other person without tipping the plank?

31.    You are working on the dock loading supplies into your boat for a fishing trip, when the boat drifts away from the dock.  You are using a uniform 12 m plank weighing 1.2 x 103 Nt to go from the dock to the boat, and the boat is located 4 m from the edge of the pier.  How far out on the plank can you walk without tipping the plank and get wet if your total mass is 65 kg?

32.    What force (FX) must be used and where must it be placed (DX) to produce total equilibrium in the following situation:

                     

33.    What force or weight must be used and where must it be placed to produce both translational equilibrium and rotational equilibrium?

          

34.   Find the tension force in the wire and the compression force in each of the following three situations:

(A)  An 11 m horizontal pole is attached by its left end to the wall of a building.  One end of a wire is attached to the wall above the pole, while the other end of the wire is attached to the free end of  the pole at an angle of 40º.  A 35 Nt sign is suspended from the free end of the pole.

(B)  Another 11 m pole projected from a wall of a shop has a support wire attached to it 8 m from the wall.  The other end of the wire makes an angle of 65º with the wall.  A 68 Nt sign is suspended from the pole’s free end.

(C)  A 11 m horizontal pole supports a sign located 8 m from the wall of a building to which the pole    is attached.  A wire is attached to the building’s wall above the pole and to the free end of the pole, making an angle of 50º.with the pole’s free end.   The sign weighs 68 Nt.

 

35.  A merchant wants to hang a 245 Nt sign from a 15 m horizontal bar which extends from the front of the store building.  A wire is to be attached to the wall of the building and to the free end of the horizontal bar such that the wire makes an angle of 38º with the bar.  The wire is unable to have a force greater than 385 Nt exerted on it without breaking.

      (A) Where must the center of gravity of this sign be suspended from the bar such that the tension in the wire will be at its maximum value?

      (B) What will be the magnitude of the compression force in this bar?

 

36.  Determine the tension in the wire and the compression in the horizontal bar for the problem below:

                

   

37. John Waffle, owner of  “Pancakes Gallery” on State Street, wants to hang a 475 Nt sign at a location of 2 m from the free end of a 16 m horizontal bar.  One end of the tie wire that supports the horizontal bar is attached to the wall and the other end is attached 4 m from the free end of the bar.  The tie wire is capable of sustaining a MAXIMUM tension of 400 Nt.  What angle must exist between the tie wire and the horizontal bar such that the tension in the wire will be a maximum value?

Go to Ladder Problem

 

Online Sources of Additional Problems:

        University of Guelph (Ontario,Canada) - PHYS 1080:  Study Guide 11.  Solve for the tension vector in problem #1 and #2.  Click on each problem's link to view its solution.

        University of Illinois - Phys 111:  Once on this home page, scroll toward the bottom of the page.  Click on "Acts".      (1) Click on "Lecture 13: Center of Mass".  Click on each of the "center of mass" activities.  the second activity is especially important for practicing the concept of "stability" discussed in your chapter notes.  (2) Click on "Lecture 20: Statics".  Click on the first "statics".  Once on "Act 2 Statics", click on "Click Here to Start".  Solve the problem, then use its associated solution slides.  Work back to the "Lecture 20: Statics" home page and click on the second "statics", which takes you to "Act 3 Statics".  Click on "Click Here to Start", which asks you to evaluate the stabiltiy of a geometric figure on an inclined surface.   Go back to Phys 111 home page, click on "Acts", then on Lecture 21: Statics.  Click on the first "Statics", then on  "Act 1 Statics", click on "Click Here to Start".  This is a "sign on a pole" problem.  Solve for the tension in the wire.  Go back to Lecture 21 and click on the second "Statics" button.  This takes you to "Act 2 Statics".  Click on "Click Here...".  This is a "mobile" problem which represents rotational equilibrium in a creative way.  Back on the Lecture 21 page, click on the third "Statics" button, which takes you to "Act 3 Statics.  This is another "sign on a pole" problem.

      The University of Cincinnati's college physics for bio/chem. Majors analyzes the torque produced by the bicepts of the human arm. (http://www.rwc.uc.edu/koehler/biophys/2h.html)

      The University of Winnipeg’s department of physics (http://physics.uwinnipeg.ca/crslinks.html).  Go to Introduction to Physics-FYDE notes- http://theory.uwinnipeg.ca/physics.  Under Table of Contents, click on “Rotational Equilibrium and Dynamics”.  Then click on “Torque” and “Another Condition for Equilibrium”. Especially click on “Problems”.  Problem 8.2 is a ladder problem. 

 

 

Multiple Choice Self-Test:    (answers listed on “Parallel Forces Test Review”)  Use available space beside each problem to write diagrams and solutions.

  1. A bar acted upon by several parallel forces will NOT rotate if:
    1. The sum of  the forces to the left of the center of gravity equals the sum of the forces to the right.
    2. The sum of the clockwise and counter-clockwise torques about the center of gravity are unequal.
    3. The sum of the clockwise and counter-clockwise torques about the center of moments are equal.
    4. The sum of the forces acting in one direction equals the sum of the forces acting in the opposite direction.
  1. The center of gravity of a body,
    1. Is measured in force units.
    2. Is measured in distance units.
    3. Remains unchanged.
    4. Is measured in mass units.

3.      A uniform bar, 10 ft in length and weighs 50-lbs has a 75-lb object attached to one end.  In order to

         balance  the bar, how far from the  attached weight must it be supported:

            a.       1 ft

            b.      1.5 ft

            c.       2 ft

            d.      3 ft

 

 

 

 

4.      A table tennis ball resting on a horizontal surface is an example of:

            a.       Stable equilibrium

            b.      Unstable equilibrium

            c.       Neutral equilibrium

            d.      A moment

 

 

5.      The product of a force and the length of the moment arm on which the force acts, is called:

            a.       Composition

            b.      The center of moments

            c.       Torque

            d.      A couple

 

 

6.      A uniform board 3.2 m long and weighs 1.4 x 103 Nt.  The minimum force required to lift one end of the

         board is:

            a.       900 Nt

            b.      700 Nt

            c.       500 Nt

            d.      350 Nt

 

 

 

7.      The weight of a painter on a scaffold and the forces exerted on the supporting ropes illustrates:

            a.       Center of gravity

            b.      Parallel forces

            c.       The fulcrum

            d.      Components of forces 

 

 

 

8.      To make an object more stable:

            a.       Decrease the size of its base.

            b.      Raise its center of gravity.

            c.       Turn it up on end.

            d.      Enlarge its base and lower its center of gravity.

 

 

9.      If a string is attached to a meter stick of unknown composition at its center of gravity and an upward pull

         is exerted:

            a.       The stick will rotate about its center of gravity.

            b.      The string will break.

            c.       The stick will rise without any rotation.

            d.      One end of the stick will be raised.

 

 

 

10.  A cone resting on its slant side is an example of which form of equilibrium:

            a.       Stable

            b.      Neutral

            c.       Unstable

 

 

 

11.  In order to have equilibrium among parallel forces:

            a.       The center of gravity must not be raised

            b.      The sum of the clockwise torques must equal the sum of the counter-clockwise torques.

            c.       The sum of the opposite forces must be equal.

            d.      The condition of “B” and “C” must both be satisfied.

 

 

 

12.  A boy and a man are supporting a 60-lb box by passing a uniform 9 ft pole through a loop of rope attached

       to the box.  What force must the boy exert when the loop is 3 ft from the man’s end?

            a.       360-lb

            b.      360 ft-lb

            c.       200-lb

            d.      20-lb

 

 

 

13.  The pole in problem #12 weighs 16-lb.  The total force which the man must exert is:

            a.       48-lb

            b.      48 ft-lb

            c.       480-lb

            d.      252-lb

 

 

 

14.  A football balanced on one end is an example of which form of equilibrium:

            a.       Stable

            b.      Neutral

            c.       Unstable

 

 

 

15.  The parallel component of an object’s weight on an inclined plane:

            a.       Distorts the shape of the incline.

            b.      Tends to make the object slide down the incline.

            c.       Is the pull of gravity toward the center of the Earth.

            d.      Is perpendicular to the surface of the incline.