A branch of a tree grows out from the trunk at an angle of 26.0° above the horizontal. Two children hang by their hands from the branch of the tree. The first child has a mass of 43.0 kg and hangs 1.40 m from the tree trunk, as measured along the length of the branch. The second child, with a mass of 34.5 kg, hangs 1.95 m from the tree trunk, also measured along the branch. Determine the magnitude (in N · m) of the net torque exerted on the branch by the children, about an axis located where the branch joins the tree trunk and is perpendicular to the plane formed by the branch and the trunk.

Q: Determine the magnitude and angle 0 of F, given that the resultant force from the three forces…

A: Write the given forces, and their x- and y-components as follows.

Q: B1-1. A connection point has two force vectors with the magnitudes of F1 = 37 kN and F2 = 24 kN. The…

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Q: An object of mass 20kg is at rest in equilibrium at the origin. At t=0s, a new force F ⃗(t) is…

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Q: A bag of cement weighing 400 N hangs in equilibrium from three wires. Two of the wires make angles…

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Q: The H2S molecule contains two hydrogen atoms and one sulfur atom. The position vectors of the…

A: Given:  rH1→ = 0.7i^+1.01j^+0.00k^rH2→ = 0.7i^ -1.01j^+0.00k^rS→ = 0.00i^+0.00j^+0.00k^Mass of H = 1…

Q: A 2.0-m-long rod has a density in kilograms per meter A= a + bx,where a = 1.0 kg/m, b = 1.0 kg/m2,…

A: Length of road l = 2 m λ=a+bx a = 1 Kg/m b= 1 kg/m2   First we calculate the mass of the road is…

Q: In the figure, a 785 kg construction bucket is suspended by a cable A that is attached at O to two…

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Q: Given the spatial force system, determine the resultant force and the angles they make with the…

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Q: Three forces act on the ring. If the resultant force FR has a magnitude and direction as shown,…

A: We have F1→+F2→+F3→=FR→ and given…

Q: 3.17 m beam (mass = 87.5 kg) is attached to a wall.  A cable is attached to the end of the beam and…

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Q: In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace…

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Q: y F1 13 12 5 02° FR F2 F1 = 400 N F2 = 675 N FR =933 N 02 = 45 °

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Q: A (-3; 2; 0), B (0; 0; 6), C (2; -3; 0) and D (0; -3; 0), Since FBA = 152, FBC = 201 and FBD = 192,…

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Q: A uniform beam of length 7.60 m and weight 450 N is carried by two workers, Sam and Joe, as shown in…

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Q: what is the magnitude of the resultant force acting on the pin and the angle between the resultant…

A: From the question, it is given that- F1 = 60N along 45o with +ve x-axisF2 = 50N along 15o with -ve…

Q: Problem 3. 4.1-4.3 Each of the bodies shown is homogeneous and has a mass of 30 kg. Assume friction…

A: Mass of each body(M)=30kg

Q: Two ropes are attached to a tree, and forces of F, = 2.0i + 4.0j and F2= 3.0i + 6.0j are applied.…

A: Given data:  F1 = 2.0i + 4.0j F2 = 3.0i + 6.0j

Q: 3.6 Determine the magnitude of the force F applied to the handle which will make the resultant of…

A: Given: Force F1 = 120 N. Force F2 = 240 N. Lever arm r1 = 150 mm. Lever arm r2 = 250 mm. Lever arm r…

Q: M2.2. A beam consists of two sections. Section A has a mass of 5.0 kg and a length of 3.0 m. Section…

A: Given data: The length of portion A is LA=3 m. The mass of potion A is mA=5 kg. The length of…

Q: String Number Mass Attached (kg) Force Exerted (N)  Direction (°) 1 .25 2.45 30° 2 .25 2.45 120° 3…

A: Given: For string 1: Force = 2.45 N mass = 0.25 kg Direction = 30 degree For string 2: Force = 2.45…

Q: F₂ = 600 N 45° F₁ = 800 N ·X F3 = 650 N 60°

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Q: Two molds of mass, the first m1 = 1.0 and the second, m2 = 2.0 kg, touch each other on a horizontal…

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Q: The semi-circular arch is loaded as shown in the Figure. For this problem, P1 = 1.8 kN, P2 = 0.90…

A: Three forces having magnitude P1=1.8kN, P2=0.9kN and P3=0.45kN    (1kN=103N) P1 and P3 make an angle…

Q: 3 = 37 + 4ĵ +5k and M = 31 +4ĵ +5k js; The angle made by the two vectors

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Q: When doing a 3D problem analysis of a rigid body, you have _____ scalar equations of equilibrium.…

A: 6 scalar equations

Q: A force acts at the origin of a coordinate system in a direction defined by the angles θx = 69.3°…

A: Given: The angle from the x-direction is 69.3°. The angle from the z-direction is 57.9°. The…

Q: At what angle must the 800-N force be applied in order that the resultant Rof the two forces has a…

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Q: Determine the length of member AB of the truss by first establishing a Cartesian position vector…

A: Vectors : Vectors are physical quantities that have both magnitude and direction. To add two…

Q: Two forces of magnitude 2F and the square root of F act such that the resultant force is squa root…

A: The dot product is the sum of the product of the corresponding entries  of these two sequence of…

Q: A force of 3.1 N makes an angle of 10o (counter-clockwise) with the +X axis. The Y component of the…

A: A force of 3.1 N makes an angle of 10o (counter-clockwise) with the +X axis. The Y component of the…

Q: The resultant of the concurrent forces has a magnitude of 1000 N passing through points (x₁ = 0, y₁…

A: The resultant force F = 1000 N The points are x2 = 2, y2 = 3, z2 =4 & x1 = 0, y1 = 0,z1 = 0 to…

Q: A long thin solid rod lies along the positive x-axis. One end is at x = 1.50 m and the other at x =…

A: It is given that

Q: If FB = 700 N, and Fc = 560 N, determine the magnitude and coordinate direction angles of the…

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Q: In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace…

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Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A: Given: The resultant magnitude R and the angle θ between the x-axis and the line of action of the…

Q: The linear mass density of a straight rod of length L is given by 2 = a +x (kg/m). Here x is the…

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Q: Two blocks of mass ma = 10 kg and mg = 5 kg are connected by a massless string that passes over a…

A: Static friction acts when there is a tendency of relative motion. Its magnitude is given by f=μsN

Q: Magnitude of the sum of the forces due to string 1 and 2 =  String Number Mass Attached (kg) Force…

A: Force exerted by string 1: F1 = 2.45 N along 10o from the horizontal => F1 = 2.45cos10o i^ +…

Q: Find the position of the centre of gravity of  an unequal angel section 10 cm x 16 cm x 2 cm

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Q: ma tug-or-war game on one campus, 15 students pull on a rope at both ends in an effort to displace…

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Q: The cables attached to the screw eye are subjected to the three forces shown. Express each force in…

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Q: An object weighing √3kg is placed on a horizontal rough plane as shown in the figure.  A force F is…

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Q: Given the spatial force system, determine the resultant force and the angles they make with the…

A: Unit vector in direction of F→1 = 0i+4j+6k02+42+62=  0i+2j+3k13 Unit vector in direction of F→2 =…

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics. 

Equilibrium of Forces

The tension created on one body during push or pull is known as force.