A block is suspended from a spring, causing it to displace 1.25m from equilibrium. The spring constant is 12 N / m. What is the mass of the block?

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Quizplus · Accepted Answer

The mass of the block is determined by the equation f = ma, where: f is the force, measured in Newtons (N), causing the displacement of the object m is the mass of the object, measured in meters (m) 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. The force causing displacement of the block is determined by the equation: f = kx, 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 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 meters and Newtons, so no conversions are necessary. Step 2: Recognize that the two equations for force on the block are equivalent. f = ma = kx Step 2: Substitute the known values and calculate the block's mass. Since the equations are equivalent, we can use ma=kx m (9.8 m/s²) = (1.25m)(12 N/m) m = (1.25m) (12 N/m) / (9.8 m/s²) m = 1.53 kg

A Block Is Suspended from a Spring, Causing It to Displace