With our choice of the pivot location, there is no torque either from the normal reaction force N or from the static friction f because they both act at the pivot. Now we are ready to use Figure to compute torques:. The net force on the ladder at the contact point with the floor is the vector sum of the normal reaction from the floor and the static friction forces:.
We should emphasize here two general observations of practical use. First, notice that when we choose a pivot point, there is no expectation that the system will actually pivot around the chosen point. The ladder in this example is not rotating at all but firmly stands on the floor; nonetheless, its contact point with the floor is a good choice for the pivot.
Second, notice when we use Figure for the computation of individual torques, we do not need to resolve the forces into their normal and parallel components with respect to the direction of the lever arm, and we do not need to consider a sense of the torque.
As long as the angle in Figure is correctly identified—with the help of a free-body diagram—as the angle measured counterclockwise from the direction of the lever arm to the direction of the force vector, Figure gives both the magnitude and the sense of the torque. This is because torque is the vector product of the lever-arm vector crossed with the force vector, and Figure expresses the rectangular component of this vector product along the axis of rotation.
This result is independent of the length of the ladder because L is cancelled in the second equilibrium condition, Figure. But the ladder will slip if the net torque becomes negative in Figure. This happens for some angles when the coefficient of static friction is not great enough to prevent the ladder from slipping. The forces that the door exerts on its hinges can be found by simply reversing the directions of the forces that the hinges exert on the door.
Hence, our task is to find the forces from the hinges on the door. The CM is located at the geometrical center of the door because the slab has a uniform mass density. We adopt a rectangular frame of reference with the y -axis along the direction of gravity and the x -axis in the plane of the slab, as shown in panel a of Figure , and resolve all forces into their rectangular components.
One equation is the equilibrium condition for forces in the x -direction. The second equation is the equilibrium condition for forces in the y -direction. The third equation is the equilibrium condition for torques in rotation about a hinge. Finally, we solve the equations for the unknown force components and find the forces.
From the free-body diagram for the door we have the first equilibrium condition for forces:. We select the pivot at point P upper hinge, per the free-body diagram and write the second equilibrium condition for torques in rotation about point P :. Solve the problem in Figure by taking the pivot position at the center of mass. A kg person stands 1. Find the tensions in the two vertical ropes supporting the scaffold. A The strut is 4. The strut is supported by a hinge at the wall and by a cable whose other end is tied to the wall at a point 3.
Find the tension in the supporting cable and the force of the hinge on the strut. Is it possible to rest a ladder against a rough wall when the floor is frictionless? Show how a spring scale and a simple fulcrum can be used to weigh an object whose weight is larger than the maximum reading on the scale. A painter climbs a ladder. Is the ladder more likely to slip when the painter is near the bottom or near the top?
A uniform plank rests on a level surface as shown below. The plank has a mass of 30 kg and is 6. How much mass can be placed at its right end before it tips? Hint: When the board is about to tip over, it makes contact with the surface only along the edge that becomes a momentary axis of rotation. The uniform seesaw shown below is balanced on a fulcrum located 3. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg.
What is the mass of the board? In order to get his car out of the mud, a man ties one end of a rope to the front bumper and the other end to a tree 15 m away, as shown below. He then pulls on the center of the rope with a force of N, which causes its center to be displaced 0. What is the force of the rope on the car? A uniform An If the tension in the left cable is twice that in the right cable, find the tensions in the cables and the mass of the equipment.
When the structure shown below is supported at point P , it is in equilibrium. Find the magnitude of force F and the force applied at P. The weight of the structure is negligible. To get up on the roof, a person mass The ladder rests against a plastic rain gutter, which we can assume to be frictionless.
The center of mass of the ladder is 2. The person is standing 3. Find the normal reaction and friction forces on the ladder at its base. A uniform horizontal strut weighs One end of the strut is attached to a hinged support at the wall, and the other end of the strut is attached to a sign that weighs The strut is also supported by a cable attached between the end of the strut and the wall. Assuming that the entire weight of the sign is attached at the very end of the strut, find the tension in the cable and the force at the hinge of the strut.
The total mass of the forearm and hand is 3. The uniform boom shown below weighs N. It is supported by the horizontal guy wire and by the hinged support at point A. What are the forces on the boom due to the wire and due to the support at A?
Does the force at A act along the boom? The uniform boom shown below weighs N, and the object hanging from its right end weighs N. The boom is supported by a light cable and by a hinge at the wall. Calculate the tension in the cable and the force on the hinge on the boom. Does the force on the hinge act along the boom? The center of mass of the boom is at its geometric center, and the mass of the boom is kg. For the position shown, calculate tension T in the cable and the force at the axle A.
A uniform trapdoor shown below is 1. It is supported by a single hinge H , and by a light rope tied between the middle of the door and the floor. Find the tension in the rope and the force at the hinge. A kg man walks on a sawhorse, as shown below. The sawhorse is 2. Calculate the normal reaction force on each leg at the contact point with the floor when the man is 0.
Hint: At each end, find the total reaction force first. This reaction force is the vector sum of two reaction forces, each acting along one leg. The normal reaction force at the contact point with the floor is the normal with respect to the floor component of this force. Privacy Policy.
Skip to main content. Search for:. For some systems in equilibrium, it may be necessary to consider more than one object. Identify all forces acting on the object. Identify the questions you need to answer. Identify the information given in the problem. In realistic problems, some key information may be implicit in the situation rather than provided explicitly. Set up a free-body diagram for the object. Draw a free-body diagram for the object, including only the forces that act on it.
When suitable, represent the forces in terms of their components in the chosen reference frame. As you do this for each force, cross out the original force so that you do not erroneously include the same force twice in equations.
Label all forces—you will need this for correct computations of net forces in the x — and y -directions. On the free-body diagram, indicate the location of the pivot and the lever arms of acting forces—you will need this for correct computations of torques. In the selection of the pivot, keep in mind that the pivot can be placed anywhere you wish, but the guiding principle is that the best choice will simplify as much as possible the calculation of the net torque along the rotation axis.
Set up the equations of equilibrium for the object. Use Figure to evaluate torque magnitudes and senses. Simplify and solve the system of equations for equilibrium to obtain unknown quantities. At this point, your work involves algebra only. Keep in mind that the number of equations must be the same as the number of unknowns. If the number of unknowns is larger than the number of equations, the problem cannot be solved. Evaluate the expressions for the unknown quantities that you obtained in your solution.
Your final answers should have correct numerical values and correct physical units. If they do not, then use the previous steps to track back a mistake to its origin and correct it. Also, you may independently check for your numerical answers by shifting the pivot to a different location and solving the problem again, which is what we did in Figure.
Check Your Understanding Repeat Figure using the left end of the meter stick to calculate the torques; that is, by placing the pivot at the left end of the meter stick. Show Solution Example Forces in the Forearm A weightlifter is holding a Check Your Understanding Repeat Figure assuming that the forearm is an object of uniform density that weighs 8. Check Your Understanding Solve the problem in Figure by taking the pivot position at the center of mass.
GMAT Quantitative. GMAT Verbal. BSchool Application Questions. Admitted - Which School to Choose? Forum Quiz - NEW! Error Log. Video FAQ's in 2 mins or less. How to get 6. All School Stats in One Place. MBA Deadlines List. Deadlines by School. Deadlines Chronological. Placement and Salary Trends. All School Discussions. MBA Success Stories. Submit a Free Profile Evaluation Request. Kenan-Flagler UNC. See All. Resources All Masters Program Discussions. MS Applicant Profiles - Success Stories of MS Admits.
Covid Updates from all top Masters Programs. Admission Deadlines by School. Master in Management. Master in Finance. Veritas Prep. Avanti Prep. Personal MBA Coach. Square One Prep. Stratus Admissions Counseling. Stacy Blackman Consulting. Prep MBA. Compare All. ARLee Consulting. August Academy.
Experts' Global. Fortuna Admissions. Gatehouse Admissions. Ivy Groupe. MBA Admit. MBA and Beyond. MBA Link. MBA Prep School. Menlo Coaching. Sia Admissions. Vantage Point MBA. The Red Pen. Prodigy Finance. Sallie Mae. Stratus Admissions Reviews. Student Loan Reviews. GMAT Courses. Admissions Consulting. Free Stuff. Practice Tests. GMAT Tutoring. Mobile Apps. Student Loans.
Which Course is right for you? Sign In Join now. My Profile Logout. Test's Subscription Expires:. Chat notifications Settings Mark All Read. Global notifications Settings Mark All Read. Unanswered Active Topics. Last visit was: Nov 12, am It is currently Nov 12, am. Decision Tracker. My Rewards. New posts. New comers' posts. Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions.
We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History.
0コメント