Objectives

1. Test the accuracy of a force sensor
2.  Test Newton’s 1^st and 2^nd laws by comparing force and acceleration for a cart on a track

Resources

• Cart with force sensor attached
• Flat cart track
• Motion Sensor
• ScienceWorkshop interface and DataStudio software
  • setup file: force_accel.ds
• Digital scale
• 50g mass holder and additional masses (50g, 100g)

Background

Isaac Newton is credited with the first mathematical formulation of the laws of motion that were already well-understood at the time. The first law states that an object that feels no force will have unchanging velocity. The second is that an object that feels a net force F will have an acceleration a proportional to its mass m F=ma The phrase “net force” is important, as the acceleration is the result of the vector sum of all forces on the object in question.

Method

To check the measurements produced by the force sensor, hang different masses from the cart’s force sensor as shown in the image. In this situation the sensor’s acceleration is zero because your hand is counteracting the force of gravity acting on the sensor and masses, but the sensor will only register the force of the masses pulling down against its hook due to the gravitational force on the masses. The “tare” button recalibrates the sensor causing whatever force the sensor is feeling when the button is pressed to register as zero Newtons.

With the cart on the track as shown, measure the data from the force sensor and acceleration from the motion sensor simultaneously while you perform the following actions:

1. By pushing or pulling on the force sensor hook, move the cart with constant velocity
2. Push or pull on the force sensor hook to move the cart with constant acceleration
3. With the force sensor hook, move the cart back and forth repeatedly 8-10 times

Analysis Questions

1. When hanging different masses from the vertically-held force sensor, what value do you expect for the ratio of force to mass? Does your result agree with this value within your experimental uncertainty?
2. Do the results of your three experiments with the cart on the track agree with Newton’s first and second laws?
3. What is the constant ratio of force to acceleration in your data? To what can you compare this value, and are the two numbers in agreement?