A spring-loaded toy gun is used to shoot a ball of mass m= 1.50\\; \ m{kg} strai

Question

A spring-loaded toy gun is used to shoot a ball of mass m= 1.50; m{kg} straight up in the air, as shown in the figure. (Figure 1) The spring has spring constant k = 667; m{N/m}. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y=0 and then released, the ball reaches a maximum height h_max (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y axis. 1

1) Find v_m the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position y=0).

2) Find the maximum height h_max of the ball.

3) Which of the following actions, if done independently, would increase the maximum height reached by the ball? Check all that apply. reducing the spring constant k increasing the spring constant k decreasing the distance the spring is compressed increasing the distance the spring is compressed decreasing the mass of the ball increasing the mass of the ball tilting the spring gun so that it is at an angle heta < 90 degrees from the horizontal

Explanation / Answer

V = A? = Av[ k /m] = 0.25*v[ 667 /1.5] = 5.27 m/s. When it leaves the equilibrium position. The height it reaches is given by v^2 = 2gH. H = V^2 /2g = 5.27*5.27 / 19.6 = 1.41 m/s ===================================

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