A 60.9 kg climber is using a rope to cross between two peaks of a mountain as shown in the figure below. He pauses to rest near the right peak. Assume that the right side rope and the left side rope make angles of 26.7° and 14.33° with respect to the horizontal respectively. Find the tension in the right and left side ropes.(Enter your answer for the right side rope followed by your answer for the left side rope.)

111 N, 11 N

To solve this problem, we can analyze the forces acting on the climber using the concept of equilibrium. We'll assume there are no other forces acting on the climber except for the tension in the ropes.

First, let's draw a free-body diagram for the climber:

|
|
| F_left
|
-------------
| | F_gravity
| |
| Climber |
| |
| |
-------------
| F_right
|
|
|

Here, F_left and F_right represent the tensions in the left and right side ropes, respectively. F_gravity is the force due to gravity acting on the climber.

The weight of the climber (F_gravity) can be calculated as the product of the mass (m) and the acceleration due to gravity (g). In this case, g is approximately 9.8 m/s^2.

F_gravity = m * g

F_gravity = 60.9 kg * 9.8 m/s^2

Now, let's calculate the horizontal and vertical components of the tension forces.

For the left side rope, the horizontal component (F_left_h) is given by:

F_left_h = F_left * cos(angle_left)

Similarly, the vertical component (F_left_v) is given by:

F_left_v = F_left * sin(angle_left)

We can use these equations to calculate the horizontal and vertical components of the left side rope tension.

For the right side rope, the horizontal component (F_right_h) is given by:

F_right_h = F_right * cos(angle_right)

Similarly, the vertical component (F_right_v) is given by:

F_right_v = F_right * sin(angle_right)

We can use these equations to calculate the horizontal and vertical components of the right side rope tension.

Now, we can set up the equilibrium equations. Since the climber is not moving horizontally or vertically, the sum of the horizontal forces and the sum of the vertical forces must be zero.

Sum of horizontal forces:

F_right_h - F_left_h = 0

Sum of vertical forces:

F_right_v + F_left_v - F_gravity = 0

Now, let's substitute the equations for the horizontal and vertical components of the rope tensions into the equilibrium equations.

F_right * cos(angle_right) - F_left * cos(angle_left) = 0

F_right * sin(angle_right) + F_left * sin(angle_left) - F_gravity = 0

Now we can solve these two equations to find the values of F_right and F_left.