## 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

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).

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?

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 $s_{yc}=\frac{1}{2}gt^2$,

$s_{yb}=u\text{sin}\theta{t}-\frac{1}{2}gt^2$ and $s_{xb}=u\text{cos}\theta t$,

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

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 $\text{tan}\theta=\frac{H}{s_{xb}}$.

Hence, $s_{yc}+s_{yb}=H$!