A deep-sea fisherman struggles to bring in a big salmon (see figure below). Find the force each hand must exert on the pole if the tension in the line is 155 N. Neglect the weight of the pole and assume that the force exerted by the left hand is directed along the horizontal. (Let è = 57.00 and L = 1.25 m.)

left hand

answer

To find the force each hand must exert on the pole, we can first resolve the tension force into its horizontal and vertical components.

The tension force in the line is given as 155 N. We can calculate its horizontal and vertical components using trigonometry.

The horizontal component of the tension force can be found by multiplying the tension by the cosine of the angle it makes with the horizontal. In this case, the angle is given as è = 57.00 degrees:

F_horizontal = 155 N * cos(57.00°)

The vertical component of the tension force can be found by multiplying the tension by the sine of the angle it makes with the horizontal:

F_vertical = 155 N * sin(57.00°)

Since the force exerted by the left hand is directed along the horizontal, the force exerted by the left hand equals the horizontal component of the tension force:

Force_left_hand = F_horizontal

The force exerted by the right hand is directed in the opposite direction of the tension force, so it will have the same magnitude but opposite sign. Therefore, the force exerted by the right hand equals the negative of the horizontal component of the tension force:

Force_right_hand = -F_horizontal

Now that we have the values of the forces, we can substitute the known values and calculate the force each hand must exert.

Let's use the given values: L = 1.25 m and è = 57.00°

Calculating the horizontal component of the tension force:

F_horizontal = 155 N * cos(57.00°)
F_horizontal = 155 N * 0.5592
F_horizontal ≈ 86.61 N (rounded to two decimal places)

Therefore, the force exerted by the left hand is:

Force_left_hand = F_horizontal ≈ 86.61 N

And the force exerted by the right hand is:

Force_right_hand = -F_horizontal ≈ -86.61 N

So, the left hand must exert a force of approximately 86.61 N on the pole, while the right hand must exert a force of approximately -86.61 N on the pole.