- #1
BlueDevil14
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I have attempted to solve this problem repeatedly, but I cannot get a correct answer. Any help would be wonderful.
The Problem
A certain kind of projectile launcher has a spring constant of 50 N/m and you compress the spring 18 cm before it locks. When compressed, the spring is 2 cm tall. The piston and spring each weigh 50 g and the ball weighs 10 g. If you launch the ball vertically, what do you expect the velocity of the ball to be as it leaves the launcher? Don't forget the gravitational potential energy gained as each object's center of mass moves vertically.
The correct answer is 4.13 m/s
My attempt at a solution
Potential energy at full compression must equal kinetic energy minus gravitational potential energy at the point when the ball is released
At full compression: U = 1/2*k*d^2 - m*g*h1 where d is displacement
At release: K=.5*m*v^2 where m is effective mass (.08 kg)
U=-m*g*h2
Therefore: 1/2*k*d^2 - m*g*h1=.5*m*v^2-m*g*h2
or 1/2*k*d^2 + m*g*(h2-h1)=.5*m*v^2
Questions
1. When calculating U of gravity, should h2-h1 be equal to the displacement of the spring (that is what I have been doing) or is it the center of mass of the ball and spring?
2. Do I use the mass of the spring and ball in calculating U of gravity?
The Problem
A certain kind of projectile launcher has a spring constant of 50 N/m and you compress the spring 18 cm before it locks. When compressed, the spring is 2 cm tall. The piston and spring each weigh 50 g and the ball weighs 10 g. If you launch the ball vertically, what do you expect the velocity of the ball to be as it leaves the launcher? Don't forget the gravitational potential energy gained as each object's center of mass moves vertically.
The correct answer is 4.13 m/s
My attempt at a solution
Potential energy at full compression must equal kinetic energy minus gravitational potential energy at the point when the ball is released
At full compression: U = 1/2*k*d^2 - m*g*h1 where d is displacement
At release: K=.5*m*v^2 where m is effective mass (.08 kg)
U=-m*g*h2
Therefore: 1/2*k*d^2 - m*g*h1=.5*m*v^2-m*g*h2
or 1/2*k*d^2 + m*g*(h2-h1)=.5*m*v^2
Questions
1. When calculating U of gravity, should h2-h1 be equal to the displacement of the spring (that is what I have been doing) or is it the center of mass of the ball and spring?
2. Do I use the mass of the spring and ball in calculating U of gravity?