## Newton’s Second Law

#### Purpose

To determine the acceleration of an object sliding down a ramp**.**

#### Objectives

- To learn how to use equipment for automated data acquisition.
- To learn how to organize data.
- To learn how to plot data and analyze it using statistical methods.
- To learn how to determine physical quantities graphically.

#### Equipment

- Air pump and air track with a glider
- Pasco Mechanical Kit
- One photogate to connect to Pasco 850 Interface
- Ruler or calipers

#### Pre-lab Activity

**Derivation of the acceleration **

An object with mass *M* glides frictionlessly along a horizontal track. It is connected to a hanging object with mass *m* through a cord and a pulley as shown on the diagram. Determine the acceleration of the gliding object in the absence of friction.

*Question 1. What will be the acceleration if friction was present and the coefficient of kinetic friction is μ ?*

#### Theory

In the absence of friction, the acceleration of the glider in the diagram above is given by the formula:

,

where *M *is the mass of the glider, and *m* is the mass of the hanging object.

#### Preliminary Setup

###### Experimental Setup

**Things to watch:**

- The air track must be level!
- The photogate must blink each time a black tape portion goes through

#### Activity. Determine the acceleration of the glider.

- Set the glider along the track above the photogate.
- Turn on the air pump to level 3 and set the Pasco Software to record measurements
- Let the glider move down the track through the photogate and stop the measurements.
- Using the Pasco Software, graph the velocity vs. time measurements. Use linear fit to determine the least-square fit line and find its slope.
- The slope of that graph is the acceleration of the glider.

#### Compare the theoretical prediction with your results for the acceleration

- Use the theoretical formula and calculate the acceleration of an object sliding down an incline track
- Compare the theoretical value with your experimental result

*Question: What is the percent difference between the two values?*

#### Analysis and Assignments

If you have a large discrepancy between the measured and the calculated acceleration work on A1. below. If your measured and calculated values for the acceleration agree to within 5% or less, work on A2. below.

**A1.** (Only if you have large discrepancy between the measured and calculated values for the acceleration). Check whether any of the following factors can be accountable for the discrepancy:

- Check your calculations for the theoretical value of the acceleration.
- Incorrect slope. Level the track again and re-rerun the experiment.
- Photogate. Let the glider through the photogate and make sure the photogate blinks properly. There should be a blink (only one) for each blackened space along the picket fence.
- Presence of friction. Increase the Air Pump level to 5 or higher and re-run the experiment.
- Using heavier or lighter hanging mass and re-run the experiment.

*Question: Which of the following factors affected your measurements?*

*Question: Were you able to obtain better results and improve the agreement between the experimental and theoretical value?*

**A2. **(Only if your experimental and theoretical values for the acceleration agreed within 5%). Repeat the experiment for a different hanging mass.

The theoretical acceleration is

,