32 kg child practicing rock climbing, she feel but the rope hung on with a tension of 253N. find acceleration??
To find the acceleration, we can use Newton's second law of motion, which states that the net force acting on an object equals the mass of the object multiplied by its acceleration.
First, we need to calculate the mass of the child using the formula mass = weight / acceleration due to gravity.
Given:
Weight of the child, W = 32 kg (mass x acceleration due to gravity)
Acceleration due to gravity, g = 9.8 m/s^2
So, the weight of the child, W = 32 kg x 9.8 m/s^2 = 313.6 N
Now, we can calculate the child's mass:
Mass of the child, m = weight / acceleration due to gravity = 313.6 N / 9.8 m/s^2 ≈ 32 kg
Since the child is hanging by the rope, the tension in the rope is equal to the weight of the child, which is 313.6 N.
Now, we can calculate the net force acting on the child:
Net force, F_net = tension - weight = 253 N - 313.6 N = -60.6 N (negative because the force is acting in the opposite direction to the weight)
Using Newton's second law (F_net = m x a), we now have all the information to calculate the acceleration (a):
-60.6 N = 32 kg x a
Divide both sides of the equation by 32 kg:
a = -60.6 N / 32 kg ≈ -1.89 m/s^2
Therefore, the acceleration of the child is approximately -1.89 m/s^2 (negative because it is in the opposite direction to the weight).