A beam of length L and mass M rests on two pivots. The first pivot is at the left end, taken as the origin, and the second pivot is at a distance { from the left end. A woman of mass m starts at the left end and walks toward the right end as in the figure below. (a) When the beam is on the verge of tipping, find symbolic expression for the normal force exerted by the second pivot in terms of M, m, and g. n2 = (m+ m)g (b) When the beam is on the verge of tipping, find symbolic expression for the woman's position in terms of M, m, L, and {. (m + m)1 X = m (c) Find the minimum value of { that will allow the woman to reach the end of the beam without it tipping. (Use any variable or symbol stated above as necessary.) min =

A beam of length L and mass M rests on two pivots. The first pivot is at the left end, taken as the origin, and the second pivot is at a distance { from the left end. A woman of mass m starts at the left end and walks toward the right end as in the figure below. (a) When the beam is on the verge of tipping, find symbolic expression for the normal force exerted by the second pivot in terms of M, m, and g. n2 = (m+ m)g (b) When the beam is on the verge of tipping, find symbolic expression for the woman's position in terms of M, m, L, and {. (m + m)1 X = m (c) Find the minimum value of { that will allow the woman to reach the end of the beam without it tipping. (Use any variable or symbol stated above as necessary.) min =

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

The beam, uniform in mass, M = 47.6 kg and length L = 10.2 m, hangs by a cable supported at point B, and rotates without friction around point A. On the end far of the beam, an object of mass m = 24.3 kg is hanging. The beam is making an angle of θ = 30.9° at point A with respect to the + x-axis. The cable makes an angle φ = 21.1° with respect to the - x-axis at B. Assume ψ = θ + φ. a. Enter an expression for the lever arm for the weight of the beam, lB, about the point A. b. Find an expression for the lever arm for the weight of the mass, lm. c. Write an expression for the magnitude of the torque about point A created by the tension T. Give your answer in terms of the tension T and the other given parameters and trigonometric functions. d. What is the magnitude, in newtons, of the tension in the cable? e. Enter an expression the horizontal component of the force, Sx, that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables…
A beam, uniform in mass, M = 47.6 kg and length L = 10.2 m, hangs by a cable supported at point B, and rotates without friction around point A. On the end far of the beam, an object of mass m = 24.3 kg is hanging. The beam is making an angle of θ = 30.9° at point A with respect to the + x-axis. The cable makes an angle φ = 21.1° with respect to the - x-axis at B. Assume ψ = θ + φ. a. Enter an expression for the lever arm for the weight of the beam, lB, about the point A. b. Find an expression for the lever arm for the weight of the mass, lm. c. Write an expression for the magnitude of the torque about point A created by the tension T. Give your answer in terms of the tension T and the other given parameters and trigonometric functions. d. Enter an expression the horizontal component of the force, Sx, that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables available in the palette. e. Enter an expression for the vertical component of…
A thin circular disk of radius R and mass M has an axle through it close to its outer edge. The disk is rotated through 90 deg and then allowed to drop. (The figure shows the disk in its initial position before it is released, and its final position when point P passes through the lowest point). a) If the zero of height is taken to be the location of the COM when the disk is in its final position, what is the energy of the disk before it is release? b) What is the moment of inertia of the disk about the axle? c) What is the angular speed of the disk when it is in the final position? d) What is the speed of point P, on the outer edge of the disk, as it passes through the lowest point in its swing?
A 10-m uniform beam of weight 100 N is supported by two ropes at its ends. If a 400-N person sits at the center of the beam, what is the tension in the right rope?
A beam resting on two pivots has a length of L = 6.00 mand mass M = 87.0 kg. The pivot under the left end exerts a normal force n1on the beam, and the second pivot placed a distance ℓ = 4.00 m from the left end exerts a normal force n2. A woman of mass = 61.5 kgsteps onto the left end of the beam and begins walking to the right as in the figure below. The goal is to find the woman's position when the beam begins to tip. (b) Where is the woman when the normal force n1 is the greatest?x = ________m(c) What is n1 when the beam is about to tip?__________ N(d) Use the force equation of equilibrium to find the value of __________n2 when the beam is about to tip. __________N(e) Using the result of part (c) and the torque equilibrium equation, with torques computed around the second pivot point, find the woman's position when the beam is about to tip.________x = m(f) Check the answer to part (e) by computing torques around the first pivot point.________x = mExcept for possible slight…
A beam resting on two pivots has a length of L = 6.00 m and mass M = 94.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot placed a distance ℓ = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 51.5 kg steps onto the left end of the beam and begins walking to the right as in the figure below. The goal is to find the woman's position when the beam begins to tip. (a) Sketch a free-body diagram, labeling the gravitational and normal forces acting on the beam and placing the woman x meters to the right of the first pivot, which is the origin. (b) Where is the woman when the normal force n1 is the greatest? x = _____m(c) What is n1 when the beam is about to tip?____N(d) Use the force equation of equilibrium to find the value of n2 when the beam is about to tip.____N(e) Using the result of part (c) and the torque equilibrium equation, with torques computed around the second pivot point, find the woman's position when the beam…
The rigid rod joining the three masses in the figure below has negligible mass. It is pivoted at one end so that it can swing in a vertical plane. lf it is released from the position shown, how fast will the bottom mass be moving when the rod is vertical?
A bicycle rider has mass M. The wheels of the bicycle are at distance l apart and horizontal distance between the seat and the rear wheel is d. Use principle of virtual work to find the normal reactions on the base of the two wheels when the rider is riding steadily.
In the mechanism shown, find the force P and all reaction forces. Ignore weight forces and friction
An oversized yo-yo is made from two identical solid disks each of mass M = 1.90 kgand radius R = 10.9 cm.The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in the figure below. Take the center of the cylinder as the axis of the system, with positive torques directed to the left along this axis. All torques and angular variables are to be calculated around this axis. Light string is wrapped around the cylinder, and the system is then allowed to drop from rest. Answer these parts: (g) Eliminate ? from the rotational second law with the expression found in part (d) and find a symbolic expression for the acceleration a in terms of m, M, g, r and R. a = (h) What is the numeric value for the system's acceleration? m/s2(i) What is the tension in the string? N(j) How long does it take the system to drop 1.17 m from rest? s
Find the torque T, in Nm, that will keep the mechanism balanced at q = 30 degrees in the system shown. The limbs AE and CD are connected to each other at their midpoints, each having a length of L = 3.7 meters and a mass of m = 117 kg. The mass of the upper horizontal platform-shaped limb is 248 kg and the mass of the car is 1.123 kg and they have the centers of gravity shown in the figure.
A crane that is 10 meters long is rotating (while loaded), at 1 radians/sec. It is stopped instantly (in 0.1 radian) in the position shown. Due to momentum the load continues to swing. Ignoring the deflection of the crane for this problem. (list all assumptions). The load is 750 lbs. a) The weight of the 10 m crane boom is 3000 lb and the mass moment of inertia is 80 lb ft s^2 about the centroid. Using the parallel axis theory find the mass moment of inertia around the point of rotation. b) What forces and moments are there on the boom at the point of rotation?