Physical Measurements, Lab Experiment 4:  Newton’s Second Law

BRING THIS SHEET TO CLASS NEXT WEEK! DO NOT PREPARE A REPORT YET!

The purpose of this experiment is to study the relationship between Force (F), mass (m), and acceleration (a).

Apparatus:

A cart with bumper, add-on weights, pulley, string, timer, ticker tape, and track.

Procedure: SHARE THE DATA WITH YOUR PARTNER

I.  Constant Force:

As usual, use about 1 meter ticker tape to record the displacements in the table provided below.  You need three runs; cart, cart + one added mass, cart + two added mass.

For each run, use 70 gram (weigh it) to accelerate the system by attaching to the spring.  Record the distances between dots in the table below.  I allowed at most 8 data intervals in the table. You can include up to 8 data points.  Don’t forget; time intervals are 0.1 second. You can calculate average acceleration from the first table and use it as the acceleration in the last table. This should normally be calculated from the slopes of v-t graph; however, we will save us some time by using the average value. The attached mass should be hung over the pulley and data should be recorded after letting the pulling mass (m) fall freely from REST! Make sure that pulling mass is initially at rest, not swinging.  Record the pulling mass’s mass here_____.  Note that  Dv =v2-v1.

 M1(just cart) M2 (car +One mass) M3 (cart +two masses) Dx(cm) v=Dx/Dt (cm/s) a= Dv/Dt (cm/s/s) Dx v=Dx/Dt a= Dv/Dt (cm/s/s) Dx v=Dx/Dt a= Dv/Dt (cm/s/s) __x___ __x___ _x___

We also need to prepare another table from which a graph will be plotted.  Prepare a 1/mass versus acceleration table.  For instance, if mass is 500 grams, 1/mass is 0.002.

The mass below refers to the total mass of the cart plus the extra weight on it.

 Mass (g) 1/mass (g-1) a(cm/s/s)

Plot acceleration versus inverse mass (1/m).  You can request a graph paper, or use the computer to produce your graph.

Questions to be answered in the discussions or conclusion section:

1) Do you see a linear trend in the acceleration versus mass graph?

2) What does it imply in terms of the Newton’s second law?

II. Constant Mass:

In this section, you will maintain the total mass of the system constant, while changing the pulling mass.  You can accomplish this by using the slotted weights.  Hang slotted weight (about 100 gram+ weight holder 50 gram) at the end of the string using the weight holder.  Start with 150 gram total (weight 100 gram hanger 50 gram), and take data using the tape.  By transferring some mass from the hanging section to the top of the moving cart, repeat the experiment two more times. Each time you can take some weight so that at the end, only the hanging weight holder remains.  Fill in the table provided below with your choice of weight transfer. M1, M2, M3 refer to the total weight moving the system (slotted weight plus weight holder).  I allowed at most 8 data intervals in the table. You can include up to 8 data points.  Calculate the average acceleration, and take it as the acceleration of the system.

 M1 M2 M3 Dx(cm) v=Dx/Dt (cm/s) a= Dv/Dt (cm/s/s) Dx v=Dx/Dt a= Dv/Dt (cm/s/s) Dx v=Dx/Dt a= Dv/Dt (cm/s/s) __x___ __x___ __x___

We also need to prepare another table from which a graph will be plotted.

The mass below refers to the total mass: slotted mass plus hanger.

 Total Mass: Hanger + slotted (g) a(cm/s/s)

Make acceleration versus mass graph using the table above.

Questions to be answered in the discussion or conclusion:

1) Do you see a linear trend in the acceleration versus mass graph?

2) What does it imply in terms of the Newton’s second law?

3) Why did we transfer mass rather than just externally adding mass to the hanger?