Thanks An adventurous archaeologist crosses between two rock

An adventurous archaeologist crosses between two rock cliffs by slowly going band over hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Figure 5.38). The rope will break if the tension in it exceeds 2.50 Times 10^4 N. Our hero\'s mass is 90.0 kg If the angle theta is 10.0 degree, find the tension in the rope. Start with a free-body diagram of the archaeologist. What is the smallest value the angle theta can have if the rope is not to break? A 1130-kg car is held in place by a light cable on a very smooth (frictionless) ramp, as shown in Fig. 5.39. The cable makes an angle of 31.0 degree above the surface of the ramp, and the ramp itself rises at 25.0 degree above the horizontal. Draw a free-body diagram for the car. Find the tension in the cable. How hard does the surface of the ramp push on the car ?

Solution

5A)

(90 x 9.8) = 882N. Halve it, = 441N.
(441/(sin 10) = 2,539.617N.
To reach a tension of 25,000N. (2.5 x 10^4), the angle from horizontal would need to be arcsin (441/25,000) = 0.017 degrees.
If that was perhaps 2.50 x 10^3, the answer would be arcsin (441/2500) = 0.17 degrees.

6A)

The car will exert Weight of Car X Sin(Angle of the Ramp)
First convert to Newtons
1130kg=11300N
11300 COS(31) = 9685.99N

So the car will exert 9685.99N on the ramp surface

the tension in the cable is almost the same formula but SIN is used instead

1130kg=11300N
11300 SIN(31)=5819.930N

So the car will exert 5819.930N force down the ramp.