# To begin a game on a pinball machine, a spring-loaded plunger is loaded with a 21 g steel ball....

## Question:

To begin a game on a pinball machine, a spring-loaded plunger is loaded with a 21 g steel ball. The player pulls horizontally on the plunger knob with a force of 26 N, compressing the spring 8 cm before releasing and propelling the ball up a ramp.

a) What is the spring constant of the plunger?

b) How much work is done by the spring on the ball?

c) How fast will the ball be traveling when it leaves the spring?

## Force, Energy, and Speed

Force is the product of the mass of an object and its acceleration stated by Newton's Second Law, F = ma. The SI unit for force is the newton, N.,

Energy is the product of the force and the distance through which it moves, that is Energy = Fd. Its units are Nm.

Energy can be potential energy stored in a spring or kinetic energy, the energy of motion. The speed of an object can be calculated if its energy and mass are known.

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{Section title='answer' !!!Answer and Explanation: a. For a spring, the force and deformation are related by F = -kx, where F is the force, x is the elongation of the spring, and k is the spring constant. Since the spring is compressed, x is negative and F is positive. [{MathJax fullWidth='false' k = \frac{F}{-x}\\ k = \frac{26 N}{0.08 m} = 325 \frac {N}{m} }] b. When the spring rebounds 0.08 m, the energy impacted from the stored energy is 26 N x 0.08 m = 2.08 Nm or 2.08 J c. The kinetic energy is transferred to the pinball and can be calculated knowing that the kinetic energy is [{MathJax fullWidth='false' K.E. = \frac {1}{2} mv^2 The unit J in fundamental units is [{MathJax fullWidth='false' \frac {kg \: m^2}{s^2} }] 2.08 [{MathJax fullWidth='false' \frac{kg\:m^2}{s^2} }] = 0.021 kg x [{MathJax fullWidth='false' v^2 = 198 \{m^2}{s^2} }] v = 14.1 m/s }]