A 65-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 8.4 m/s2. Ignore the effects of air resistance.
gravity provides a downward acceleration of 9.8 m/s^2
so the bungee cord is providing an upward acceleration of 1.4 m/s^2 (9.8 - 8.4)
the force is upward
with a magnitude of 65 kg * 1.4 m/s^2
To find the force exerted on the bungee jumper by the bungee cord, you can use Newton's second law of motion which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the force will be the force exerted by the bungee cord, the mass of the jumper is 65 kg, and the acceleration is 8.4 m/s^2.
Step 1: Write down the formula for Newton's second law of motion:
F = m * a
Step 2: Substitute the given values into the formula:
F = 65 kg * 8.4 m/s^2
Step 3: Calculate the force:
F = 546 N
Therefore, the force exerted on the bungee jumper by the bungee cord is 546 Newtons. The direction of the force will be upward because it opposes the downward acceleration of the jumper.
In order to find the force exerted on the bungee jumper by the bungee cord, we need to use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
Mass of the bungee jumper (m) = 65 kg
Acceleration of the bungee jumper (a) = 8.4 m/s^2 (downward acceleration)
To find the force, we will use the formula:
Force (F) = mass (m) * acceleration (a)
Substituting the given values:
F = 65 kg * 8.4 m/s^2
F = 546 N
Therefore, the magnitude of the force exerted on the bungee jumper by the bungee cord is 546 N.
Since the bungee cord is stretching and resisting the jumper's downward motion, the force will be directed opposite to the downward motion, that is, in the upward direction.