MEQ491 Mechanics & Materials Lab

Experiment 7:
Dependent Motion of Particle

Analyze dependent motion of particles on inclined planes. Calculate displacement, velocity, acceleration, and kinetic friction coefficients through interactive simulation.

Start Simulation Lab Report
A W s h θ

1.0 Introduction

In engineering dynamics, understanding how multiple bodies move in relation to each other is fundamental. Dependent motion occurs when the motion of one particle depends on the motion of another, typically through constraints such as ropes, cables, or pulleys.

This experiment investigates the dependent motion of two connected particles: a block sliding on an inclined plane (Block A) and a set of hanging weights. The block is connected to the weights via an inextensible rope passing over a frictionless pulley at the top of the incline. When the hanging weights are heavy enough to overcome friction, the system begins to accelerate — the weights fall while Block A moves up the plane.

By measuring the displacement and time of travel, students will determine the velocity and acceleration of both the block and the weight system, and ultimately calculate the coefficient of kinetic friction (μk) between Block A and the inclined surface.

2.0 Objectives

  1. To determine the relationship between displacement, velocity, and acceleration of two dependent particles connected via a pulley system on an inclined plane.
  2. To calculate the velocity and acceleration of both Block A and the hanging weight system at different inclination angles (θ = 15° and θ = 45°).
  3. To determine the coefficient of kinetic friction (μk) between Block A and the sliding surface using experimental data and Newton's second law.
  4. To compare how the angle of inclination affects the system's acceleration and friction behaviour.

3.0 Apparatus

Equipment List

  1. Inclined plane apparatus (adjustable angle)
  2. Wooden block (Block A) — approx. 2 kg
  3. Set of slotted weights (various masses)
  4. Inextensible string/cord
  5. Frictionless pulley
  6. Stopwatch (digital)
  7. Metre ruler / measuring tape
  8. Protractor (for angle verification)
  9. Weighing scale

Setup Diagram

A W θ Pulley String

Figure 1: Experimental setup

4.0 Theory and Equations

The relationship of displacement, velocity, and acceleration between the hanging weights and Block A can be determined using Newton's second law:

ΣF = m · a

For an inextensible rope over a frictionless pulley, the displacement and velocity of the hanging weight and Block A are related directly. When Block A moves a distance s along the incline, the hanging weight descends a height h determined by the geometry.

The forces acting on Block A include its weight component along the plane (mg sin θ), the normal force (mg cos θ), the tension in the rope (T), and the friction force (Ff = μk N).

Figure 2: Free body diagram

A Ground Distance, s Height, h θ

Key Equations

Velocity of Block A, vA = s / t (1.1)
Velocity of weight, vw = h / t (1.2)
Acceleration of Block A, aA = (vA − uA) / t (1.3)
Acceleration of weight, aw = (vw − uw) / t (1.4)
Coefficient of kinetic friction, μk = Ff / N (1.5)

Where: s = distance along incline, h = height of weight drop, t = time, u = initial velocity (0 for start from rest), Ff = friction force, N = normal force = mAg cos θ.

Note

The initial velocity uA = uw = 0 since the system starts from rest. Thus: aA = vA / t and aw = vw / t.

5.0 Interactive Simulation

Simulate the dependent motion system. Set the angle, add weight, and release to observe the behaviour.

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TIME 0.00s
DIST 0.00m
A
W

Score

0 pts

6.0 Daily Life Game: Laundry Line Challenge

Predict how a simple clothesline with two baskets behaves when their masses change. Reinforces dependent motion intuition.

L
R

Two baskets connected by a rope over a roof

Press "Start Round" to generate basket masses.

Left Basket

- kg

Right Basket

- kg

Your Prediction:

Game Score

0 pts

7.0 Concept Check Quiz

Answer 5 questions to test your understanding of dependent motion and the sliding system.

Quiz Score

0 pts

1. In a dependent motion system, when Block A moves 0.5 m down the incline, the hanging weight will:

2. Increasing the angle of the incline (from 15° to 45°) generally causes the acceleration of Block A to:

3. The main purpose of using the time and distance data from the simulation is to determine:

4. In the laundry line game, if both baskets have the same mass, the system will:

5. For Block A on an incline, the component of its weight pulling it down the plane is:

Laboratory Rubric

Criteria Item Score 5 (Excellent) Score 4 (Good) Score 3 (Satisfactory) Score 2 (Poor) Score 1 (Very Poor)
1. Org & AppearancePerfect sequence. Intact diagrams. Clean headers. Typed cover. Single PDF.Format good. 1 detail missing. Tape bound.Rough format. Multiple errors. Stapled no bind.Sloppy. Damaged inserts. Poor staple.Absent.
2. ObjectivesRephrased own words. Linked to research.Identified. Manual paraphrase.Partial definition. Manual copy.Verbatim copy. Missing content.Absent.
3. ApparatusListed. Labeled diagrams. Steps own words. Safety photo.Vital items. Paraphrased steps. No photo.Partial list. Confusing steps.Missing equipment. Unusable.Absent.
4. Results (×2)Accurate trends. Tables numbered. Walkthrough examples. Equations used.Correct trends. Minor label gaps. Formulas provided.Missing data. Sloppy tables. Units missed.Bad construction. Unreliable data.Absent.
5. Discussion (×2)Answers all. Links theory. Errors analyzed.Misses one. Gaps in interpretation.Incomplete logic. Shallow depth.Lack understanding. Incorrect comparison.Absent.
6. ConclusionSummarizes data. Validates objectives. Suggestions logic.Missing 1 condition.Missing 2 conditions.Missing 3 conditions.Absent.
7. References>9 sources. Standard format. 30% recent.6–8 sources. Manual format.3–5 sources. Partial compliance.1–2 sources. Format ignored.None.

Lab Report (Softcopy)

Fill the data tables, then print or export as PDF.

MEQ491: Mechanics & Materials Lab

Experiment 7: Dependent Motion of Particle

4.0 Theory

Figure 2: Dependent motion

Ashθ

ΣF = ma. Velocity and acceleration calculated using:

vA = s / t
(1.1)
vw = h / t
(1.2)
aA = vA / t
(1.3)
aw = vw / t
(1.4)
μk = Ff / N
(1.5)

5.0 Procedure

  1. Select suitable inclination angle, θ (15° and 45°).
  2. Add the weights until Block A begins to move along the incline.
  3. Pull Block A to a starting mark and measure height, h.
  4. Release Block A and start the stopwatch simultaneously.
  5. Stop the watch once the weight hits the table.
  6. Record the time, distance s, weights and mass of Block A.
  7. Repeat the experiment by adding more weight.

6.0 Result

Table 1: Experimental Data

Weight, W (N) Distance, s (m) Time, t (s)
123Avg 123Avg

Table 2: Calculation Data

Weight, W (N)
(1) (2) (3) (4) (5) (6)
vA (m/s)
vw (m/s)
aA (m/s²)
aw (m/s²)
μk

Table 2 values auto-calculated from Table 1 (v = s/t, a = v/t, assuming u = 0).

7.0 Discussion

i) Draw the free body diagram and kinetic diagram for Block A and the weight.

ii) Compare and discuss the displacement, velocity, and acceleration of Block A at 15° and 45°.

iii) Compare and discuss the coefficients of kinetic friction at each angle.

iv) Comment on any causes of errors.

8.0 Conclusion

9.0 References

Data Analysis Portal

Enter simulation results to calculate μk.

Calculated Friction (μk)

0.00

Final Submission

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