Question

a block of known mass hanging from an ideal spring of known spring constant is oscillating vertically. a motion detector records the position, velocity, and acceleration of the block as a function of time. which of the following indicates the measured quantities that are sufficient to determine whether the net force exerted on the block equals the vector sum of the individual forces? responses acceleration only acceleration only acceleration and position only acceleration and position only acceleration and velocity only acceleration and velocity only acceleration, position, and velocity

Answer 1

Answer: Acceleration and position only

Explanation: Although it might seem as though the question is asking you to prove that the sum of all individual forces equal the net force, but this is not the case. Instead the question means to ask "What is needed to calculate net force?" and "What is needed to calculate the individual forces?" For the first question, net force can be calculate from the equation "F = m * a", where F is net force, m is mass, which is known, and a is acceleration. To determine F, acceleration must also be known. For the second part of the question, it is important to note that the only forces acting on the block are gravity (F = m * g) and the spring force (F = -kx). m is already known; g, acceleration due to gravity, is always 9.8 m/s^2 unless otherwise specified; and k, the spring constant, is known. This leaves x, the position. So, the position must also be known. There you have it; we must know both the acceleration and position to determine the equality of net force and the individual forces in this case.