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An archer must exert a force of 385 N on the bowstring shown in Figure (a) such that the string makes an angle of ? = 32.5° with the vertical.

(a) Determine the tension in the bowstring.

____________N

(b) If the applied force is replaced by a stretched spring as in Figure (b) and the spring is stretched 32.0 cm from its unstretched length, what is the spring constant?

____________N/m

Explanation / Answer

here,

force applied , F = 385 N

theta = 32.5 degree

(a)

let the tension in the string be t

2 * t * sin(theta) = F

2*t * sin(32.5) = 385

t = 358.27 N

the tension in the bowstring is 358.27 N

(b)

elongation in the spring , x = 0.32 m

applied force , F = 385 N

let the spring constant be k

k*x = F

k*0.32 = 385

k = 1203.13 N/m

the spring constant is 1203.13 N/m

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