PHYS 154 – University Physics – Laboratory – Lab Form Spring 2019

1

weight hook and 50-g base

center pin and ring

force-table protractor

clamp with pulley

LAB 06 – Net Forces

Group: __________

Names: _________________________ _________________________ __________________________

(Principle Coordinator) (Lab Partner) (Lab Partner) Goals:

Understand the concept of net force in the context of Newtonian perspective about motion

Revisit and practice vector calculation and measurement

Apply the students’ knowledge about vector manipulation to the calculation and measurement of net forces.

Scenario and Strategy:

Imagine a situation where a body is under the combined action of two or three forces with known magnitudes and directions.

Your task is to find the net force acting on the object for an ulterior motive, such as to figure out the ensuing acceleration, or

to apply a fourth force and keep the object in mechanical equilibrium.

You will have to add the vectors in three sets of two and three vectors

As explained in the pre-lab, the vectors to be analyzed are given by their magnitude (given as a weight, so you will know

can calculate the necessary mass) and direction (as a standard position angle measured counterclockwise)

You will first find the resultant using graphical and analytical methods. Then you shall re-obtain it using direct

measurement

To reinforce the concept of vector component, you shall also take a vector through a process of resolution

Equipment and Handling:

Welch force table, pulleys, center ring and pin

String, weight hooks, assortment of weights

Ruler, protractor

Force Table

This is a classic instrument for the study of equilibrium of forces

The forces are emulated using weighs pulling on a central ring

using strings passing over pulleys. The direction is set by moving

the pulley-clamps around the degree-scale on the table

The forces are in equilibrium if the ring doesn’t touch the center

pin and circles it symmetrically

For example, the forces in the figure are in equilibrium because

their magnitude is the same (the hooks hold the same 50-g mass)

and they have symmetric directions at standard position angles 0º,

90º, 180º, and 270º

Measuring Resultants using a Force Table:

Note that each force in such a static equilibrium is the equilibrant

of the others. That is, it cancels the resultant of the other forces, so

it can be used to find the respective resultant

For example, if three forces �⃗�1, �⃗�2, and �⃗�3 are in equilibrium, then any of the three is the equilibrant of the other two

For instance, �⃗�3 is the equilibrant of �⃗�1 and �⃗�2. Therefore, if it is a force of magnitude measured by a hanging weight

𝑚𝑔, and a direction 𝜃:

3 ,F mg

then the resultant �⃗⃗� = �⃗�1 + �⃗�2 is the opposite of the equilibrant, given by

, 180R mg .

PHYS 154 – University Physics – Laboratory – Lab Form Spring 2019

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PART 1: Finding the resultant of three sets of given forces

Set 1: 1 1 , 2.45 N,30F m g 1 250 gm

2 2 , 2.45 N,120F m g 2 250 gm

Graphical method:

Use the adjacent frame to find the resultant by the tail-to-tip

method. Use the scale 1 cm = 0.4 newton (the grid boxes may not

be exactly one centimeter, but don’t worry about that; use a ruler)

Label the forces �⃗�1 and �⃗�2, and the resultant �⃗⃗�1

Determine the magnitude of the resultant by measuring its length in

cm and multiplying it by 0.4 N/cm

Measure its standard position angle using a protractor

Fill the numbers in the table at the end of the procedures

Analytical method:

Calculate the x- and y-components of the two vectors and use them

to calculate the components of the resultant

Use the components of the resultant to find its magnitude and

direction

Show your calculations in the space provided

Fill the numbers in the table at the end of the procedures.

Experimental analysis:

For �⃗�1, clamp a pulley at 30°. Tie a string between the 50 g weight

hook and the center ring to drape the hook over the pulley

To build this force, you will place a 200-g weight on the weight

hook yielding a force of 2.45 N. However, do not place the weights

on the hook now, wait until instructed to do so in the next steps.

Just sketch �⃗�1 on the circular graph on the right

For �⃗�2, attach a pulley clamped at 120°, and a string and weight

hook tied to the center table ring. Once again, be ready to place a

200 gram weight on the weight hook yielding a force of

approximately 2.45 N. But not yet. Just sketch �⃗�2 on the circular

graph on the right

As explain above, the resultant of two or more force vectors is

found by balancing the forces with an equilibrant force vector �⃗�𝑒

Sketch �⃗�𝑒 on the circular graph on the right at an angle that you

consider appropriate to balance �⃗�1 + �⃗�2

Clamp a pulley at the equilibrant angle. Add a string and a hook and

drape it over the pulley

At this point, add masses to the hooks for �⃗�1 and �⃗�2 as appropriate.

Then add masses to the hook associated with force �⃗�𝑒, until the

system appears to be balanced around the pin on the table. When

your system is in balance, record the mass of the equilibrant and

determine the weight associated with that mass

Using the equilibrant, determine the resultant vector �⃗⃗�1. Sketch it

on the circular graph. Fill its magnitude and direction in the table at the end of the procedures

Reapply the procedures described above to the following two sets of forces. For both sets, show your calculations for the

analytical method in the space provided on the next page

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6 7

y (N)

x (N)

PHYS 154 – University Physics – Laboratory – Lab Form Spring 2019

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Set 2: 1 1 , 1.96 N,20F m g 1 200 gm

2 2 , 1.47 N,80F m g 2 150 gm

Set 3: 1 1 , 0.980 N,30F m g 1 100 gm

2 2 , 1.96 N,90F m g 2 200 gm

3 3 , 2.94 N,330F m g 3 300 gm

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9

y (N)

x (N)

0

1

2

3

4

5

6

0 1 2 3 4 5 6

y (N)

x (N)

PHYS 154 – University Physics – Laboratory – Lab Form Spring 2019

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1. Calculations: For all three sets, show your calculations for the analytical method in the space provided below

Set 1:

Set 2:

Set 3:

2. Results:

3. Conclusions: Discuss some error sources affecting your measurements in this lab, and summarize what you learned

Set Forces Graphical

Resultant

Analytical

Resultant

Experimental Resultant

Mass m and angle 𝜽 needed to

produce the equilibrant. Compute

the corresponding resultant.

Within experimental

uncertainty, was

�⃗⃗⃗�𝒆 ≈ −�⃗⃗⃗� ?

(Circle one)

Set 1 �⃗�1= (2.45N, 30°)

�⃗�2= (2.45N, 120°) 𝜃1 =

𝑅1=

𝜃1 =

𝑅1=

𝑚 =

𝜃 = ] → [

𝑅1 =

𝜃 1=

�⃗�𝑒 ≈ −�⃗⃗�1

�⃗�𝑒 ≠ −�⃗⃗�1

or

Set 2 �⃗�1= (1.96N, 20°)

�⃗�2= (1.47N, 80°)

𝑅2= 𝜃2 =

𝑅2= 𝜃2 =

𝑚 =

𝜃 = ] → [

𝑅2 =

𝜃 2=

�⃗�𝑒 ≈ −�⃗⃗�2

�⃗�𝑒 ≠ −�⃗⃗�2

or

Set 3

�⃗�1= (0.98N, 30°)

�⃗�2= (1.96N, 90°)

�⃗�3= (2.94N, 330°)

𝑅3= 𝜃3 =

𝑅3= 𝜃3 =

𝑚 =

𝜃 = ] → [

𝑅3 =

𝜃 3=

�⃗�𝑒 ≈ −�⃗⃗�3

�⃗�𝑒 ≠ −�⃗⃗�3

or

PHYS 154 – University Physics – Laboratory – Lab Form Spring 2019

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PART 2: Vector Resolution

Note: This problem is not the same as the previous examples. You are given a single force and will calculate the x- and

y-components of the vector. You will then determine the equilibrant vectors to each of the two components to see if it

balances the single original force

You are given with the vector: , 2.94 N,60F mg 250 gm

Graphical Resolution:

Draw �⃗� on the adjacent frame. Label it with its symbolic name, �⃗�

Drop a vertical to the x-axis from the tip of the vector arrowhead. The

displacement along the x-axis is the horizontal component 𝐹𝑥. Measure it with

your rule and use your scaling factor to determine its value in newtons

Draw a horizontal from the y-axis to the arrowhead. The displacement along the

y-axis is the vertical component 𝐹𝑦. Once again, determine it with a rule and

your scaling factor

Analytical Resolution:

Compute 𝐹𝑥 and 𝐹𝑦 by mathematically calculating the x- and y-components of

vector �⃗�, using the usual trigonometric formulas

Show you calculation in the space below:

Experimental Resolution:

Clamp pulleys at 60°, 180°, and 270° on the force table

Place a total of about 300 grams on the 60° weight hanger including the hanger; this is force �⃗�

Place weights on the 180° hanger and the 270° hanger until the system is in equilibrium.

The force at 180° is the equilibrant of 𝐹𝑥. That is, 𝐹𝑥 has the same magnitude but points in the opposite direction, 0°

The force at 270° is the equilibrant of 𝐹𝑦. That is, 𝐹𝑦 has the same magnitude but points in the opposite direction, 90°

Enter your 𝐹𝑥 and 𝐹𝑦-component magnitudes from all three methods in the table below

Force Graphical

Resolution

Analytical

Resolution

Experimental Resolution

Mass needed to

produce the

equilibrant

Within experimental uncertainty, were the

equilibrants equal to −𝑭𝒙 or −𝑭𝒚?

(Circle one)

Record your equilibrant if significantly different

�⃗� = (2.94 N, 60°)

𝐹𝑥 =

𝐹𝑦 =

𝐹𝑥 =

𝐹𝑦 =

𝑚𝑥 =

𝑚𝑦 = 𝐹𝑒𝑥 =

𝐹𝑒𝑦 =

𝐹𝑒𝑥 ≈ −𝐹𝑥 and 𝐹𝑒𝑦 ≈ −𝐹𝑦 or

𝐹𝑒𝑥 ≠ −𝐹𝑥 or/and 𝐹𝑒𝑦 ≠ −𝐹𝑦

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5

y (N)

x (N)