1 A climber of mass 80 kg is on a steep rock face. The force X
that the rock exerts on the climber is at an angle of 50° to
the vertical. Y, the other force on the climber, keeps himin
equilibrium and is provided by a rope at an angle of 40° to the
vertical.
a) Draw a sketch to show the forces acting on the climber.
b) From your sketch of the forces, sketch a triangle of forces to
show equilibrium.
)Use your triangle of forces to find
1) X, the force the rock face exerts on the climber
i) Y, the force provided by the rope
a)
b)
1) X = 80 kg * 9.8 m/s^2 * sin(50°) = 745.6 N
ii) Y = 80 kg * 9.8 m/s^2 * sin(40°) = 645.6 N
1 A climber of mass 80 kg is on a steep rock face. The force X
that the rock exerts on the climber is at an angle of 50° to
the vertical. Y, the other force on the climber, keeps himin
equilibrium and is provided by a rope at an angle of 40° to the
vertical.
a) Draw a sketch to show the forces acting on the climber.
b) From your sketch of the forces, sketch a triangle of forces to
show equilibrium.
)Use your triangle of forces to find
1) X, the force the rock face exerts on the climber
i) Y, the force provided by the rope
a) Here is a sketch showing the forces acting on the climber:
```
X (rock face force)
/
/
/
/_ 50°
/
/
------------------
\
\
\
\ Y (rope force)
\
\
\_ 40°
```
b) From the sketch above, we can now draw a triangle of forces to show equilibrium:
```
X (rock face force)
/
/
Y /____ 50°
/
/
------------------
\
\
\
```
To find X and Y, we can use the triangle of forces:
Using the law of sines, we can write:
sin(50°) / X = sin(40°) / Y
Now we can solve for X and Y:
X = (sin(50°) * Y) / sin(40°)
Y = (sin(40°) * X) / sin(50°)
```
Let me know if I can assist you with anything else.
a) To explain how to draw a sketch to show the forces acting on the climber, follow these steps:
1. Start by drawing a vertical line to represent the rock face.
2. At the top of the line, draw a line at an angle of 50° to represent force X. Label it as X.
3. At the bottom of the vertical line, draw a line at an angle of 40° to represent force Y. Label it as Y.
4. Connect the two ends of forces X and Y to form a triangle.
This sketch represents the forces acting on the climber: force X from the rock face and force Y from the rope.
b) To create a triangle of forces to show equilibrium, follow these steps:
1. Start with the sketch of forces X and Y from step a.
2. Draw a third line from the end of force X to the end of force Y.
3. Label this line as Z.
This triangle represents the equilibrium of the climber, where forces X, Y, and Z are balanced.
To find the values of X and Y, we can use trigonometry and the triangle of forces:
1) X, the force the rock face exerts on the climber:
- Use the triangle of forces to identify the angle opposite to force X, which is the angle between forces X and Z.
- Apply trigonometry, using the known angle and the length of force Y. You can use the sine or cosine rule to calculate force X.
i) Y, the force provided by the rope:
- Use the triangle of forces to identify the angle opposite to force Y, which is the angle between forces Y and Z.
- Apply trigonometry, using the known angle and the length of force X. Again, you can use the sine or cosine rule to calculate force Y.
By using trigonometry and the triangle of forces, you can find the values of X and Y, which represent the forces acting on the climber.