A spring loaded toy gun is used to shoot a ball of mass m=1.50kg straight up in

Question

A spring loaded toy gun is used to shoot a ball of mass m=1.50kg straight up in the air. The spring has a spring constant k=667 N/m. If the spring is cmpressed a distance of 25.0 centimeters from its equilibrium position y=0 and then released, the ball reaches a maximum height. There is no air resistance, and the ball never touches the inside of thegun. assume that all movement occur in a straight line up and down along the y axis. Part A: Which of the following statements are true? A)Mechanical energy is conserved because no dissipative forces perform work on the ball. B)The forces of gravity and the spring have potential energies associated with them c) No conservative forces act in this problem after the ball is released from the spring gun. PART B Find v/m the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position ). y=0 PART C Find the maximum height of the ball. PART D 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 0 <90 degrees from the horizontal .

Explanation / Answer

1 a)true b)true c)false, gravity is a conservative force 2. first find energy of the spring with E=1/2*k*x^2 = 20.84 J assuming its 100% efficient and all work is transferred as kinetic energy, we can use the equation KE=1/2*m*v^2 v=sqrt(2*Ke/m) = 5.27 m/s 3. we use 2*a*x=v^2-v0^2 x=(v^2-v0^2)/(2*a) = v0^2/(2*g) = 0.289 m a) reducing the spring constant k - no b) increasing the spring constant k - yes c) decreasing the distance the spring is compressed - no d) increasing the distance the spring is compressed - yes e) decreasing the mass of the ball - yes f) increasing the mass of the ball - no g) tilting the spring gun so that it is at an angle theta < 90 degrees from the horizontal - no

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