A spring-loaded toy gun is used to shoot a ball of mass straight up in the air,

Question

A spring-loaded toy gun is used to shoot a ball of mass straight up in the air, as shown in the figure. The spring has spring constant . If the spring is compressed a distance of 25.0 centimeters from its equilibrium position and then released, the ball reaches a maximum height (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.
A)Find the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position ).
B)Find the maximum height of the ball.
C)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
increasing the spring constant
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 degrees from the horizontal

Explanation / Answer

a) using the conservation of energy: the energy before = energy after 1/2 k x^2 = 1/2 m v0^2 , where x is the amount of compression in the spring solving for v0 (muzzle velocity) we get: sqrt(k/m) * x B) from kinematics: v^2 = v0^2 + 2a(y), we want to look at the ball when v = 0.. --> 0 -v0^2 = 2a(y) solving to the height y we get -v0^2/2a = y but remember that a = -g, therfore: y = v0^2/2g C) looking at the equation v0 = sqrt(k/m) x, decreasing k would decrease the muzzle velocity and therefore decrease the height. from the same equation above, x is proportional to v0 therefore decreasing x result in smaller y. decreasing the mass means increasing the quantity sqrt(k/m) which is proportional to v0, therefore would result in a height shot. increasing the mass is just the opposite of decreasing it. since the potential energy coming from the spring wont change by tilting the gun, the only way to gain a component in the x-direction is for the ball to take from the kinetic energy, resulting in less energy in the y-direction and therefore smaller height. hope that helps ..

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.