PHYS.1310 TECHNICAL PHYSICS I LAB

SIMULATION – MOTION ON AN INCLINED PLANE

INTRODUCTION

The objective of this simulation lab is to study, predict and quantify the motion of objects down

an inclined plane. The acceleration of a block down the incline will be measured as function of

angle.

THEORY

Consider a block of mass, M on an inclined plane having ? as the angle of the incline, (neglect any

frictional forces). See the diagram below.

Note that the axes have been rotated by the angle ? of the inclined plane so that the positive x

direction is down the plane and the positive y direction is perpendicular to the plane as shown.

The free body diagram for the block indicates that there are two forces acting on it:

N = Normal Force (perpendicular to the inclined plane)

Mg = Weight of the block (vertically downwards)

Let’s apply Newton’s 2nd Law to the block. This results in the following two equations:

? ???? = ???? and ? ???? = ????

???? ??????(??) = ???? and ?? ? ???? ??????(??) = 0

? ?? = ?? ??????(??) ……… (1)

From Equation (1) it can be seen that the acceleration of the block depends only on the angle and it is

independent of the mass of the block.

PHYS.1310 TECHNICAL PHYSICS I LAB

SIMULATION – MOTION ON AN INCLINED PLANE

Suppose we consider the case where there is a frictional force between the block and the inclined plane.

???? ? ?????? model used for static friction (when there is no relative motion between block and plane) ???? ? ?????????????????????? ???? ???????????? ????????????????

???? = ?????? model use for kinetic friction (when there is relative motion between block and plane) ???? ? ???????????????????? ???? ?????????????? ????????????????

Suppose we begin by having the angle at zero degrees and increase it, the block will not start to move until a

certain angle is reached (at this point the static frictional force is a maximum)

Let’s again apply Newton’s 2nd Law to the block, which then results in the following two equations:

? ???? = ???? and ? ???? = ????

???? ??????(??) ? ???? = 0 and ?? ? ???? ??????(??) = 0

At this angle, where the block just begins to move, the static frictional force is equal to its maximum.

Combining these two equations results in the following

µ?? = ??????(??) …….. (2)

f s

PHYS.1310 TECHNICAL PHYSICS I LAB

SIMULATION – MOTION ON AN INCLINED PLANE

MEASUREMENTS

Use the link below to begin taking measurements.

https://ophysics.com/f2.html

Note: The following six parameters may be varied: ??, ????, ???? , ????, ??, ??

Part A: The dependence of acceleration on the angle of incline.

1. Set the initial values of the parameters to:

? = angle of incline = 10o

vo = initial velocity of the block = 0 m/s

µk = coefficient of kinetic friction = 0

µs = coefficient of static friction ~ 0

m = mass of the block = 5 kg

g = free fall acceleration = 9.8 m/s 2

https://ophysics.com/f2.html
PHYS.1310 TECHNICAL PHYSICS I LAB

SIMULATION – MOTION ON AN INCLINED PLANE

2. Simulation for above set of parameters

? Note down the angle you have set (10o) and the mass of the block (5 kg).

? Create a data table -1 –> include time and position, ???, ???, velocity.

? Press “Run” and “Pause” – to note down the initial time (t) and displacement (x) values.

? Repeat “Run and Pause” – and get 5data points.

3. Simulation changing the angle.

? Set the angle of incline to 15o.

? Note down the angle you have set (15o) and the mass of the block (5 kg).

? Create a data table -2 –> include time and position, ???, ???, velocity.

? Run the simulation (as before) and get 5 data points.

Part B: The dependence of acceleration on the mass of the block.

? Use the last angle from above (15o).

? Change the mass to m = 10 kg

? Create a data table -3 –> include time and position, ???, ???, velocity.

? Run the simulation (as before) and get 5 data points.

Part C: The effect of friction (Demo)

With the angle of incline as 15o and mass = 10kg:

? With coefficient of friction µs and µk both as zero:

– Run the simulation and make an observation of the motion of the block.

? Change the µs to different value (~0.5):

– Run the simulation to determine the maximum value of

the angle, ? when the block does not move.

– Make a note of this angle and the corresponding µs.

PHYS.1310 TECHNICAL PHYSICS I LAB

SIMULATION – MOTION ON AN INCLINED PLANE

RESULTS AND ANALYSIS

Part A:

1) For the 1st angle, complete the data tables 1 and 2.

2) Plot a graph of velocity versus time.

3) Determine the slope of this graph. What does this give you?

4) For your inclined plane setup, the theoretically expected acceleration of the block can be calculated using

equation (1).

5) Repeat steps 2 to 4 for the 2nd.

6) Compare the measured accelerations versus the expected values.

Part B:

1) Complete the data table 3.

2) For the data with two different masses (keeping the same angle), plot the graph of velocity vs. time.

Determine the acceleration value from the slope of this graph.

3) How does the acceleration value compare for 5kg-block and 10-kg block? Does it support the theory?

Part C:

1) You obtained ? for a certain set value µs.

2) Compare the above µs -value to the one from calculated using equation (2).

QUESTIONS

1. Why are the axes rotated from the usual orientation? Would any of your results be different if the axes were not rotated? Explain.

2. Describe and explain how the frictional force changes as the angle of the inclined plane increases.

Is the explanation different for kinetic friction versus static friction?