An archer draws his compound bow and shoots an arrow. The 23 g arrow leaves the bow with a velocity of 88 m/s. The power stroke of the bow is 57 cm; that is, the bowstring exerts force on the arrow through a displacement of 57 cm. The peak draw weight of the bow is 312 N. (This is the maximum force that the archer has to exert on the bowstring.)

Question

Physics

Saunders

2 May, 13:07

An archer draws his compound bow and shoots an arrow. The 23 g arrow leaves the bow with a velocity of 88 m/s. The power stroke of the bow is 57 cm; that is, the bowstring exerts force on the arrow through a displacement of 57 cm. The peak draw weight of the bow is 312 N. (This is the maximum force that the archer has to exert on the bowstring.)

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Answers (1)

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Sandra Bradshaw · Answer 1

156.24N

Explanation:

From the data above;

Mass = 23g = 0.023kg

V = 88m/s

Kinetic energy = ½mv²

K. e = ½ * 0.023 * 88²

K. E = 89.056J

The force required to accelerate the arrow to that speed and energy in 0.57m

Using equation of motion;

V² = U² + 2as

But U = 0

V² = 2as

a = v²/2s

a = 88² / (2*0.57)

a = 6792.98m/s²

The force (F) that accelerates the arrow with that velocity = ?

F = M*a

F = 0.023 * 6792.98

F = 156.24N