A 200-g block is suspended from a spring, causing it to stretch 10 cm from equilibrium. What is the spring constant for this spring?

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The spring constant is determined by the equation k = f/x, where: k is the spring constant, measured in Newtons per meter (N/m) f is the force, measured in Newtons, applied to the spring x is the distance of displacement from equilibrium, measured in meters The force is determined by the equation f = ma, where: f is the force, measured in Newtons, causing the displacement of the object m is the mass of the object, measured in meters a is the acceleration of the object, measured in meters per second squared (m/s²) Note: Since the object in this scenario is hanging from the spring, the acting force is gravity. The acceleration for any object moving under the sole influence of gravity (i.e. hanging from a spring) is the gravitational constant which is 9.8 m/s². Step 1: Determine the values provided in the problem and convert units to match the units used in the standard equations. Remember, we are measuring: f (force) in Newtons (N) x (distance of displacement from equilibrium) in meters (m) m (mass of object) in kilograms (kg) a (acceleration of object) in meters per second squared (m/s²⁾ The word problem provides information using grams and centimeters, so we need to convert them to kilograms and meters: Mass of the block = 200 g x (1 kg / 1000 g) = 0.200 kg Distance from equilibrium = 10 cm x (1 m / 100 cm) = 0.1 m Step 2: Find the force in Newtons by multiplying the gravitational constant by the block's mass. f = ma f = 0.2 kg (9.8 m/s²) = 1.96 N Step 3: Calculate the spring constant. k = f/x k = 1.96 N / 0.1 m k = 19.6 N / m

A 200-G Block Is Suspended from a Spring, Causing It