A 65-kg bungee jumper, who is attached to one end of an 85-m long bungee cord that has its other end tied to a bridge, jumps off
the bridge and toward the river below. When stretched, the bungee cord acts like a spring and provides a force on the jumper that increases linearly as the cord is stretched. When the bungee cord is stretched to its maximum length, it exerts a 2.2 kN force on the jumper. If the bungee cord is stretched beyond its equilibrium length for a duration of 1.2 seconds, what is the impulse delivered to the bungee jumper
1 answer:
Answer:
The impulse delivered to the bungee jumper is 1.32 kN.s
Explanation:
The situation can be shown graphically as shown in the figure.
Impulse delivered to the bungee jumper = Area under the curve.
The curve represents a triangle and the area of traiangle = (1/2)base×height
The base of the triangle from the graph = 1.2 seconds.
The height of the triangle from the graph = 2.2 kN
Thus,
<u>Impulse = (1/2)×(1.2 seconds)×(2.2 kN) = 1.32 kN.s</u>
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The spring will come to rest 4.9 m below the natural length
Explanation:
The mass-spring system will come to rest when the restoring force on the spring (pulling upward) balances the weight of the mass (pulling downward). Mathematically, this can be written as
where
k is the spring constant
x is the elongation of the spring
m is the mass
g is the acceleration of gravity
In this problem, we have:
is the mass
is the acceleration of gravity
is the spring constant
Solving the equation for x,
Therefore, the spring will come to rest 4.9 m below the natural length.
Learn more about forces:
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