Two forces of 55N and 85N act on an object simultaneously and the resultant force is 125N. What is the measurement of the angle between the two forces?

Expert Solution

Denote the angle by θ.

Start with a parallelogram rule. The sum vector is along the diagonal of the parallelogram, splitting the parallelogram into two triangle with sides of lengths 55, 85, and 125. The angle opposite to the side of length 125 is π - θ radians. Now apply the law of cosines to finish.

1252 = 552 + 852 - 2*55*85 cos(π - θ)

15625 = 3025 + 7225 - 9350 cos(π - θ)

cos(π - θ) = 5375/9350 = -215/374

cos θ = 215/374

θ = 0.95835 radians ( 54.90972 degrees )

54.9°

Nipun Maity answered 2 years ago

Determine the magnitude of the resultant force. Determine the coordinate direction angle α of the resultant force.

Determine the magnitude of the resultant force. Determine the coordinate direction angle α of the resultant force. Determine the coordinate direction angle β of the resultant force.Determine the coordinate direction angle γ of the resultant force.

A: Three forces act on a moving object. One force has a magnitude of 86.0 N...

A: Three forces act on a moving object. One force has a magnitude of 86.0 N and is directed due north. Another has a magnitude of 64.5 N and is directed due west. What must be the magnitude and direction of the third force, such that the object continues to move with a constant velocity? B: A worker stands still on a roof sloped at an angle of 39.1° above the horizontal. He is prevented from slipping by a static...

The screw eye is subjected to the two forces shown. Express each force in Cartesian vector form and then determine the resultant force

The screw eye is subjected to the two forces shown. Express each force in Cartesian vector form and then determine the resultant force. Find the magnitude and coordinate direction angles of the resultant force.

What is the difference between a stabilizing force and dislocating force? At what angle of pull...

What is the difference between a stabilizing force and dislocating force? At what angle of pull does the stabilizing force become a dislocating force? Why? For full credit, draw the free body diagrams and equations of force or moment to support your answer.

Schematically show (1) forces (including all components and resultant force) at the tool-chip surface, (2) forces...

Schematically show (1) forces (including all components and resultant force) at the tool-chip surface, (2) forces (including all components and resultant force) at the material shear plane, and (3) depth of cut and chip thickness of orthogonal cutting.

1. Two forces P and Q act on an object of mass 20.0 kg with Q...

1. Two forces P and Q act on an object of mass 20.0 kg with Q being the larger of the two forces. When both forces are directed to the left, the magnitude of the acceleration of the object is 0.900 m/s2. However, when the force P is directed to the left and the force Q is directed to the right, the object has an acceleration of 0.400 m/s2 to the right. Find the magnitudes of the two forces P...

1. Several forces act on an object at rest. It is known that the sum of...

1. Several forces act on an object at rest. It is known that the sum of the forces acting on the object is zero. Which statement is necessarily true? A) The object will remain stationary. B) The object's center of mass may move in such a way that the object will roll without slipping. C) The object's center of mass will not move, but the object may begin to rotate. D) The object's center of mass may accelerate and the...

Create a plot comparing the force applied to an object versus the angle at which the...

Create a plot comparing the force applied to an object versus the angle at which the force is applied. Alos, plate describe the graph in paragraph form.

Find the magnitude and direction of the resultant of two concurrent forces of 50 and 75...

Find the magnitude and direction of the resultant of two concurrent forces of 50 and 75 N acting on a body at angle of 50 degrees with each other Use the graphical method and the algerbraic method

Three forces are applied to an object, as indicated in the drawing. Force F with arrow1...

Three forces are applied to an object, as indicated in the drawing. Force F with arrow1 has a magnitude of 22.0 newtons (22.0 N) and is directed 30.0° to the left of the +y axis. Force F with arrow2 has a magnitude of 16.3 N and points along the +x axis. What must be the magnitude and direction (specified by the angle θ in the drawing) of the third force F with arrow3 such that the vector sum of the...

Question