A 49-kg bungee jumper has fallen far enough that her bungee cord is beginning to stretch and resist her downward motion. Find the force (magnitude and direction) exerted on her by the bungee cord at an instant when her downward acceleration has a magnitude of 7.3 m/s2. Ignore the effects of air resistance. Take the upward direction as positive.
To find the force exerted on the bungee jumper by the bungee cord, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). In this case, the downward acceleration of the bungee jumper is given as 7.3 m/s^2.
The force exerted by the bungee cord can be calculated as follows:
F = m * a
Now, to find the force, we need to know the mass (m) of the bungee jumper. The problem states that her mass is 49 kg.
Substituting the known values into the equation:
F = 49 kg * 7.3 m/s^2
Calculating the value:
F = 357.7 N
Therefore, the magnitude of the force exerted on the bungee jumper by the bungee cord is 357.7 Newtons.
Now, let's determine the direction of the force. The problem states that the upward direction is positive. Since the bungee cord is exerting a force to prevent the downward motion, the force exerted by the bungee cord will be in the upward direction. Thus, the force exerted on the bungee jumper by the bungee cord is positive.