Question

A mountain climber of mass m hangs onto a rope to keep from sliding down a smooth, ice covered slope. Find the formula for the tension in the rope when the slope is inclined at an angle θ above the horizontal. Check your results in the limits θ=0 and θ=90degrees.  

Answer 1

Solution :

Here, The forces along the plane acting on the man of mass m are :

• T (up the plane) and,
• mg sin θ (down th plane).

And, The net force acting onthe man is : mg sin θ - T (down the plane).

If this is zero he may climb down with unifor velocity, a = 0.

If a > 0, then

Net force, mg sinθ - T = ma

T = mg  sinθ - ma = m ( g sinθ - a)

.

For θ = 90 : vertically down.

Since : sin(90) = 1

T = m (g - a) = m g (if a = 0)

For θ = 0 :

mg sin(0) = 0 (no force acting).

No downward motion.