in preparation in shooting a pinball machine, a spring(k = 675N/m) is compressed by 0.0650m relative to its unstrained lenght.the ball(m = 0.0585kg) is at rest against the spring at point A. when the spring is released ,the ball
To determine the speed of the ball when it is released from the spring, you can use the principle of conservation of mechanical energy. This principle states that the total mechanical energy of a system remains constant as long as no external forces are acting on it.
In this case, the only force acting on the ball is the spring force. The spring force can be expressed as:
F = -kx
Where F is the force, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
Since the ball is at rest against the spring at point A, the spring is compressed by 0.0650m. This means that the displacement x is 0.0650m.
Now, let's calculate the potential energy stored in the compressed spring. The potential energy can be given by:
PE = (1/2)kx^2
Substituting the known values:
PE = (1/2)*(675 N/m)*(0.0650 m)^2
PE = 0.0348 J
According to the conservation of mechanical energy principle, this potential energy will be converted into kinetic energy when the ball is released.
Kinetic energy can be expressed as:
KE = (1/2)mv^2
Where KE is the kinetic energy, m is the mass of the ball, and v is the speed of the ball.
Equating the potential and kinetic energies:
PE = KE
0.0348 J = (1/2)*(0.0585 kg)*(v^2)
Now, let's solve for v:
v^2 = (2*0.0348 J) / (0.0585 kg)
v^2 = 3.000 J/kg
v = sqrt(3.000 J/kg)
v ≈ 1.73 m/s
So, when the ball is released from the spring, it will have a speed of approximately 1.73 m/s.