An archer pulls a bowstring back by a distance of 0.56 m. The bowstring has a force constant of 340 N/m.
(a) What force is exerted by the archer?
(b) What is the elastic potential energy of the bowstring?
a) The force exerted by the archer is 191.4 N.
b) The elastic potential energy of the bowstring is 193.6 J.
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To calculate the force exerted by the archer, you can use Hooke's Law, which states that the force exerted by a spring or elastic material is directly proportional to the displacement from its equilibrium position. The formula is:
F = k * x
where F is the force exerted, k is the force constant, and x is the displacement.
Given:
Force constant (k) = 340 N/m
Displacement (x) = 0.56 m
(a) To calculate the force exerted by the archer, plug the given values into the formula:
F = 340 N/m * 0.56 m
F ≈ 190.4 N
Therefore, the force exerted by the archer is approximately 190.4 N.
(b) The elastic potential energy of the bowstring can be calculated using the formula:
Potential Energy (PE) = (1/2) * k * x^2
Given:
Force constant (k) = 340 N/m
Displacement (x) = 0.56 m
(b) To calculate the elastic potential energy of the bowstring, plug the values into the formula:
PE = (1/2) * 340 N/m * (0.56 m)^2
PE ≈ 52.79 J
Therefore, the elastic potential energy of the bowstring is approximately 52.79 Joules.
To answer these questions, we can use Hooke's Law, which states that the force exerted by a spring or elastic material is directly proportional to the displacement or deformation from its equilibrium position.
(a) What force is exerted by the archer?
We can use Hooke's Law to determine the force exerted by the archer. The formula for Hooke's Law is:
F = k * x
where F is the force exerted, k is the force constant (also known as the spring constant) of the bowstring, and x is the displacement or deformation of the bowstring.
In this case,
k = 340 N/m (given)
x = 0.56 m (given)
Plugging in these values into the formula, we have:
F = 340 N/m * 0.56 m
F = 190.4 N
Therefore, the force exerted by the archer is 190.4 N.
(b) What is the elastic potential energy of the bowstring?
The elastic potential energy of a stretched or compressed spring is given by the formula:
PE = (1/2) * k * x^2
where PE is the elastic potential energy, k is the force constant, and x is the displacement or deformation of the spring.
Using the given values of k = 340 N/m and x = 0.56 m, we can calculate the elastic potential energy:
PE = (1/2) * 340 N/m * (0.56 m)^2
PE = 53.92 J
Therefore, the elastic potential energy of the bowstring is 53.92 Joules.