Concept explainers
A stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = ℓ = 4.00 m. A painter of mass m = 70.0 kg stands on the ladder d = 3.00 m from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.
(a)
The tension experienced on the horizontal bar
Answer to Problem 73P
The tension experienced on the horizontal bar
Explanation of Solution
From the geometry of the ladder the angle
First of all consider the net torque at the point A which is at the bottom left side of the ladder. The torque experienced at this point is due to the weight of the painter, and the normal force at point B,
Write the expression for the torque at point A.
Here,
The net torque at point A is zero, hence equate equation (I) to zero and obtain an expression for
Now consider the net torque acting at the point B, which is at the bottom right of the ladder. The torque at point B same as A, is due to the weight of the painter and normal force at point A,
Write the expression for the net torque at point B.
The net torque acting at point B will be zero, equate equation (III) to zero, and obtain an expression for
Consider the torque at the point Cat the top of the right half of the ladder. At this point torque is due to the tension,
Write the expression for the torque at point C.
The net torque at point C is zero. Equate equation (III) to zero, and obtain an expression for
Substitute, equation (II) in (VI).
The tension
Write the expression for the force acting along right.
Equate equation (VIII) to zero.
Write the expression for the force acting along
Equate equation (VIII) to zero.
From equation (XI) the reaction force
Conclusion:
Substitute,
Therefore, the tension experienced on the horizontal bar
(b)
The normal force acting at A, and B.
Answer to Problem 73P
The normal force acting at A is
Explanation of Solution
Use equation (II) and (IV) to obtain the answer.
Conclusion:
Substitute,
Substitute,
Therefore, the normal force acting at A is
(c)
The components of reaction forces at point C.
Answer to Problem 73P
The components of reaction forces at point C are,
Explanation of Solution
Consider equation (IX) and (XI), the
The tension experienced on the horizontal bar
The normal force acting at B is
Conclusion:
Therefore, the components of reaction forces at point C are,
Want to see more full solutions like this?
Chapter 10 Solutions
Principles of Physics: A Calculus-Based Text
- 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 OQ10.9arrow_forwardA uniform beam resting on two pivots has a length L = 6.00 m and mass M = 90.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot located a distance = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 55.0 kg steps onto the left end of the beam and begins walking to the right as in Figure P10.28. The goal is to find the womans position when the beam begins to tip. (a) What is the appropriate analysis model for the beam before it begins to tip? (b) Sketch a force diagram for the beam, labeling the gravitational and normal forces acting on the beam and placing the woman a distance x to the right of the first pivot, which is the origin. (c) Where is the woman when the normal force n1 is the greatest? (d) What is n1 when the beam is about to tip? (e) Use Equation 10.27 to find the value of n2 when the beam is about to tip. (f) Using the result of part (d) and Equation 10.28, with torques computed around the second pivot, find the womans position x when the beam is about to tip. (g) Check the answer to part (e) by computing torques around the first pivot point. Figure P10.28arrow_forwardFrom the step ladder shown in the figure, sides AC and CE are each 2.44 m long and hinged at point C. Bar BD is a tie-rod 0.762 m long, halfway up. A man weighing 845 N climbs 1.8 m along the ladder. Assuming the floor is frictionless and neglecting the mass of the ladder, find the tension (in N) in the tie-rod.arrow_forward
- A uniform beam of length L = 2.2 m and mass M = 33 kg has its lower end fixed to pivot at a point P on the floor, making an angle θ = 15° as shown in the digram. A horizontal cable is attached at its upper end B to a point A on a wall. A box of the same mass M as the beam is suspended from a rope that is attached to the beam one-fourth L from its upper end.What is the y-component Py of the force, in newtons, exerted by the pivot on the beam? Py = Write an expression for the tension T in the horizontal cable AB. T = What is the x-component Px of the force, in newtons, exerted by the pivot on the beam? Px =arrow_forwardFor a rigid body in equilibrium, identify the true statements about the action of a system of external forces. (Check all that apply.) It imparts translational motion. It imparts rotational motion. It imparts no rotational motion. It imparts no translational motion.arrow_forwardA uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. Since the floor is rough, it exerts both a normal force N1 and a frictional force f1 on the ladder. However, since the wall is frictionless, it exerts only a normal force N2 on the ladder. The ladder has a length of L = 4.4 m, a weight of WL = 53.5 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m = 90kg is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N1 = ? N N2 = ? N f1 = ? N (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N1 = ? N N2 = ? N f1 = ? Narrow_forward
- Why is the following situation impossible? A uniform beam of mass mb = 3.00 kg and length ℓ = 1.00 m supports blocks with masses m1 = 5.00 kg and m2 = 15.0 kg at two positions as shown. The beam rests on two triangular blocks, with point P a distance d = 0.300 m to the right of the center of gravity of the beam. The position of the object of mass m2 is adjusted along the length of the beam until the normal force on the beam at O is zero.arrow_forwardAs shown in the figure below, a stick of length L = 0.410 m and mass m = 0.180 kg is in contact with a rough floor at one end and a frictionless bowling ball (diameter d = 20.00 cm) at some other point such that the angle between the stick and the floor is ? = 30°.Determine the following. (a) magnitude of the force exerted on the stick by the bowling ball N(b) horizontal component of the force exerted on the stick by the floor N(c) vertical component of the force exerted on the stick by the floor Narrow_forwardA person is standing on a section of uniform scaffolding as shown in the figure. The section of scaffolding is L = 1.50 m in length, has a ms = 24.5 kg mass and is supported by three ropes as shown. Determine the magnitude of the tension in each rope when a person with a weight of Wp = 640 N is a distance d = 0.700 m from the left end. magnitude of T1 N magnitude of T2 N magnitude of T3 Narrow_forward
- A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. Since the floor is rough, it exerts both a normal force N1 and a frictional force f1 on the ladder. However, since the wall is frictionless, it exerts only a normal force N2 on the ladder. The ladder has a length of L = 4.1 m, a weight of WL = 61.0 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m = 90 kg is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N1 = N N2 = N f1 = N (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N1 = N N2 = N f1 = Narrow_forwardA 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?arrow_forwardA bar weighing 26.0 N is supported horizontally on each end by two hangingsprings, each 15.0 cm long, with spring constants 0.970 N/cm and 1.45 N/cm,respectively. The bar is 6.00 m long and has a center of mass 2.00 m from thespring with constant 0.970 N/cm. How far does each spring stretch?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning