A student sets up an experiment to determine the inertial mass of a cart

Question

The student has access to the following measurement equipment: a spring scale, a meterstick, and a stopwatch. The student uses the spring scale to pull the cart starting from rest along a horizontal surface such that the reading on the spring scale is always constant. All frictional forces are negligible. In addition to the spring-scale reading, which two of the following quantities could the student measure with the available equipment and then use to determine the inertial mass of the cart? Select two answers.

1. 
   
2. A) The total distance traveled by the cart after it has been in motion
3. B) The average speed of the cart while in motion
4. C)The acceleration of the cart while in motion
5. D)The time during which the cart is in motion

Answer 1

Recall that whenever we measure anything with spring scales we are measuring FORCES. the reading on the spring scale will be units of force.

Recall Newton's second law which states that the general force of an object is the objects mass multiplied by it's acceleration

F = (m)(a)

We know the measured force thanks to the spring scale. Releasing it will cause the object to move back to rest. As the object moves we can use the meter stick and stop watch to measure it's ACCELERATION. once found we just divide the force by this measured value to get the second inertial mass.

Springs have their own way of measuring force. Experimentally it was found that the force exerted on a spring always varies linearly with respect to DISPLACEMENT from rest

F = (-k)(x)

k is known as the spring constant intrinsic to every spring. The negative sign arises from the spring always tryig to restore itself to it's initial position.

Basically what the equation says is that the more we displace a spring(stretch or compress) the more force to will exert to restore itself.

Because our example the spring was stretched and pulled by some x amount, we just need to measure the distance it has been displaced from the center.

Once we have both the DISPLACEMENT of the spring and ACCELERATION. We can then set the equations equal to each other to calculate the mass

In short the answer is A and B