An archer pulls her bowstring back 0.420 m by exerting a force that increases uniformly from zero to 240 N.
(a) What is the equivalent spring constant of the bow?
N/m
(b) How much work does the archer do in pulling the bow?
J
work= INT force dx=INT 240x/.420 dx
work= 1/2 240*.420=120*.420
that equals 1/2 k x^2
120*.420=1/2 k .420^2
k= 240/.420 N/m
To find the equivalent spring constant of the bow (k), we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
(a) To find the spring constant (k), we can use the formula:
k = F / x
where F is the force applied and x is the displacement.
In this case, the force increases uniformly from zero to 240 N, and the displacement is 0.420 m.
k = 240 N / 0.420 m
Calculating this, we get:
k = 571.43 N/m
Therefore, the equivalent spring constant of the bow is 571.43 N/m.
(b) To find the work done by the archer, we can use the formula for work:
Work = Force x Distance
In this case, the force applied is changing from zero to 240 N, and the distance over which the force is applied is 0.420 m.
As the force increases uniformly, we can find the average force by taking the average of the initial and final forces:
Average force = (0 + 240) / 2 = 120 N
Now, we can substitute the values into the work formula:
Work = Average force x Distance
Work = 120 N x 0.420 m
Calculating this, we get:
Work = 50.4 J
Therefore, the archer does 50.4 Joules of work in pulling the bow.