To hoist himself into a tree, a 72.0-kg man ties one end of a nylon rope around his waist and throws the other end over a branch of the tree. He then pulls downward on the free end of the rope with a force of 365 N. Neglect any friction between the rope and the branch, and determine the man’s upward acceleration. Use g=9.81m/sec2.
To determine the man's upward acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the net force acting on the man is the tension in the rope pulling him upward, minus his weight pulling him downward. Let's calculate these forces:
Weight (W) = mass (m) x gravitational acceleration (g)
W = 72 kg x 9.81 m/s^2
W = 706.32 N
Net force (F_net) = tension in the rope (T) - weight (W)
F_net = 365 N - 706.32 N
F_net = -341.32 N (negative because it acts in the opposite direction of the acceleration)
Now, we can use Newton's second law to find the man's upward acceleration (a):
F_net = m x a
-341.32 N = 72 kg x a
Solving for a, we get:
a = -341.32 N / 72 kg
a = -4.74 m/s^2
The man's upward acceleration is approximately -4.74 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the force applied.