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?A. Acceleration only B. Acceleration and position only C. Acceleration and velocity onlyD. Acceleration, position, and velocityPart 1. “Whether The net force exerted on the block equals the vector sum of the individual forces” really means “Newton’s Second Law”. The problem wants you to make measurements to show that the net force equals mass times acceleration. How would you find the force exerted by the spring? How do you find the force exerted by gravity? Part 2. Connect your answer to the previous question with the right answer. Clearly explain which quantities must be measured (between acceleration, velocity, and position) and explain what each quantity is used for to show Newton’s second law.

Answer 1

B. Acceleration and position only

Step-by-step explanation:

We need to identify the measurements that show that the net force is equal to the sum of the force exerted by the spring and the force of gravity, so we want to know if the following equation is satisfied

`\begin{gathered} F_(net)=F_s-mg \\ ma=k(\Delta x)-mg \end{gathered}`

Where m is the mass, a is the acceleration, k is the spring constant, Δx is the stretched, and g is the gravity. The mass m, the spring constant k, and the gravity g are known. So, the measurement quantities that we need are the acceleration and the position.

So, the answer is

B. Acceleration and position only

Part 1.

How would you find the force exerted by the spring?

The force exerted by the spring is equal to k(Δx ), so to find Δx, we need to identify the position.

How do you find the force exerted by gravity?

The force exerted by gravity is calculated as mass times gravity, so it is known.

Part 2.

We need to measure Acceleration and position.

The acceleration to calculate the net force because by the second law of newton Fnet = ma

The position to calculate the force exerted by the spring.