Newton's 2nd Law Experiment using Motion Sensor

For my students: To download the file and video for analysis using Tracker, right-click the file here...


To verify the equation F = ma, where F is the resultant force on an object, m is the mass of the object and a is the acceleration, this is one of the ways to do so:

Equipment:
1. Motion Sensor
2. Datalogger
3. Cart with variable mass
4. End Stop
5. Pulley with clamp
6. Hanger Mass Set
7. String (about 1.2 m)

For a system of a cart of mass M on a horizontal track that is connected to a hanging mass m with a string over a pulley, the net force F on the entire system (cart and hanging mass) is the weight of hanging mass. F = mg (no friction assumed).

newton 2nd law experiment

According to Newton’s Second Law, mg = (M+ m)a. We will try to prove experimentally that this is true in the video below.

2-Dimensional Kinematics Problem: Shooting a dropping coconut

The following is a question (of a more challenging nature) posed to JC1 students when they are studying the topic of kinematics.

A gun is aimed in such a way that the initial direction of the velocity of its bullet lies along a straight line that points toward a coconut on a tree. When the gun is fired, a monkey in the tree drops the coconut simultaneously. Neglecting air resistance, will the bullet hit the coconut?

coconut kinematics
Two-Dimensional Kinematics: Gun and Coconut Problem

It is probably safe to say that if the bullet hits the coconut, the sum of the downward displacement of coconut s_{yc} and the upward displacement of the bullet s_{yb} must be equal to the initial vertical separation between them, i.e. s_{yc}+s_{yb}=H. This is what we need to prove.

Since s_{yc}=\dfrac{1}{2}gt^2s_{yb}=u\text{sin}\theta.t-\dfrac{1}{2}gt^2 and s_{xb}=u\text{cos}\theta t,

s_{yc}+s_{yb}=u\text{sin}\theta\times t=u\text{sin}\theta\times \dfrac{s_{xb}}{u\text{cos}\theta}=s_{xb}\times{\text{tan}\theta}.

At the same time, the relationship between H and the horizontal displacement of the bullet s_{xb} before it reaches the same horizontal position of the coconut is \text{tan}\theta=\dfrac{H}{s_{xb}}.

Hence, s_{yc}+s_{yb}=H!