1,Aclimber Of Mass 80Kg Is On A Steep Rock Face.The Force X That The Rock Exerts On The Climber Is At An Angle Of 50 degree To The Vertical.Y,the Other Force On The Climber,keeps Him In Equilibrium&is Provided By Arope At An Angke Of 40 Degree To The Vertical.
A,draw Asketch To Show The Force Acting On The Climber?
B,from Your sketch Of The Forces,sketch Atriangle Of Force To Show Equilibrium?
C,Use Your Triangle Of Forces To Find.
I,X,The Force The Rock Face Exerts On The Climber?
II,Y,the Force Provided By The Rope?
answer please
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A) To draw a sketch of the forces acting on the climber, we need to represent the force exerted by the rock face (X) and the force provided by the rope (Y).
Since the force X is at an angle of 50 degrees to the vertical and the force Y is at an angle of 40 degrees to the vertical, the sketch would look something like this:
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-----C----- Climber
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\|/Y
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\|/X
B) To sketch a triangle of forces to show equilibrium, we need to use the given angles and label the sides of the triangle with the corresponding forces. The triangle should be closed to represent equilibrium.
X
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Y | \ Y
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X X
C) Using the triangle of forces, we can find the values of X and Y:
I) To find the force X, we can use trigonometry. From the triangle of forces, we can see that the angle opposite to X is 90 - 50 = 40 degrees.
sin(40) = X / 80 Kg (mass of climber)
X = 80 * sin(40)
X ≈ 51.65 Kg
II) To find the force Y, we can use the same trigonometric approach. From the triangle of forces, we can see that the angle opposite to Y is 90 - 40 = 50 degrees.
sin(50) = Y / 80 Kg (mass of climber)
Y = 80 * sin(50)
Y ≈ 61.23 Kg
Therefore, the force X that the rock face exerts on the climber is approximately 51.65 Kg, and the force Y provided by the rope is approximately 61.23 Kg.
A. To draw a sketch showing the forces acting on the climber, we need to consider the given information. The force X exerted by the rock is at an angle of 50 degrees to the vertical, and the force Y provided by the rope is at an angle of 40 degrees to the vertical.
Draw a vertical line representing the vertical direction. From the bottom end of this line, draw a line inclined at an angle of 50 degrees to the vertical. Label this line as X to represent the force exerted by the rock. From the bottom end of the vertical line, draw another line inclined at an angle of 40 degrees to the vertical. Label this line as Y to represent the force provided by the rope.
B. To sketch a triangle of forces to show equilibrium, we need to add another line representing the resultant force. The resultant force is the vector sum of forces X and Y.
From the end point of X, draw a line parallel to Y. From the end point of Y, draw a line parallel to X. These lines will intersect at a point, which represents the resultant force. Connect this point to the starting point (where the vertical line begins) to complete the triangle.
C. Now, using the triangle of forces, we can find the magnitudes of forces X and Y.
I. To find the magnitude of force X (the force exerted by the rock face on the climber), measure the length of the line segment representing X in the triangle of forces.
II. To find the magnitude of force Y (the force provided by the rope), measure the length of the line segment representing Y in the triangle of forces.