(7%) Problem 10: A dart gun includes a spring of spring constant k = 19 Nm which

Question

(7%) Problem 10: A dart gun includes a spring of spring constant k = 19 Nm which is used to fire a dart of mass m. The dart leaves the gun at a speed of v = 3.5 m/s after the spring is compressed 1 cm ©theexpertta.com - 33% Part (a) What is the weight, F, in Newtons, of the dart? -.. 33% Part (b) What is the dart's speed when it hits the floor vr in m/s, if it is fired horizontally at a height of h = 2 meters? 33% Part (c) what angle, in degrees, does the dart's final velocity make with the horizontal? Grade Summary Deductions 100% Potential 0%

Explanation / Answer

here,

spring constant , K = 19 N/m

speed , v = 3.5 m/s

x = 0.01 m

a)

let the mass be m

using conservation of energy

0.5 * k * x^2 = 0.5 * m * v^2

19 * 0.01^2 = m * 3.5^2

solving for m

m = 1.55 * 10^-4 kg

the weight , W = m * g = 1.52 * 10^-3 N

b)

let the time taken to hit the ground be t

h0 = 0 + 0.5 * g * t^2

2 = 0 + 0.5 * 9.81 * t^2

t = 0.64 s

the dart's final vertical speed , vy = 0 + g * t = 6.26 m/s

vx = 3.5 m/s

the final speed , |v| = sqrt(vx^2 + vy^2)

|v| = sqrt(3.5^2 + 6.26^2) = 7.18 m/s

c)

theta = arctan(vy/vx)

theta = arctan(6.26 /3.5) = 60.8 degree below the horizontal

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