A mass of 7.80 kg on a horizontal surface is pushed against a spring with an elastic constant of 985 N/m untilthe spring is compressed a distance of 35.0 cm from its equilibrium position. The mass is re/eased and thespring expands, causing the mass to accelerate. When the spring has pushed the mass a distance of 5.00 cm,the mass has a speed of 2.00 m/s. At this point of its acceleration, the mechanical energy of the mass isJ. (Record your three-digit answer on the answer sheet.)
Question
A mass of 7.80 kg on a horizontal surface is pushed against a spring with an elastic constant of 985 N/m untilthe spring is compressed a distance of 35.0 cm from its equilibrium position. The mass is re/eased and thespring expands, causing the mass to accelerate. When the spring has pushed the mass a distance of 5.00 cm,the mass has a speed of 2.00 m/s. At this point of its acceleration, the mechanical energy of the mass isJ. (Record your three-digit answer on the answer sheet.)
Solution
The mechanical energy of the mass can be calculated by adding the kinetic energy and the potential energy of the mass at the given point.
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Calculate the kinetic energy (KE) using the formula KE = 1/2 * m * v^2, where m is the mass and v is the speed. KE = 1/2 * 7.80 kg * (2.00 m/s)^2 = 15.6 J
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Calculate the potential energy (PE) stored in the spring using the formula PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement from the equilibrium position. PE = 1/2 * 985 N/m * (0.05 m)^2 = 1.23 J
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Add the kinetic and potential energy to get the total mechanical energy. Mechanical Energy = KE + PE = 15.6 J + 1.23 J = 16.83 J
So, the mechanical energy of the mass at the given point is approximately 16.83 J.
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