# The acceleration of an Object on a frictionless incline

Physics 201 Fundamentals of Physics I Lab

FALL 2018

Name:

W # :

Section: Time: Date:

Lab partner:

Lab # 2

I

The Equation of Motion of a Uniformly

Accelerated Object in 1D

Purpose:

Introduction The motion of an object moving in 1D subjected to a uniform acceleration (from a uniform force) is described by the following Equation of Motion

Position: x(t) = x0 + v0 t + ½ a t2

Velocity: v(t) = v0 + a t

Procedure:

Data

Mcart = 0.515 kg , mhanging = 0.05 kg ; a = mg / ( m+M )

 x(t) (m) t(s) t1 t2 t3 tavg v(m/s) v1 v2 v3 vavg

Analysis and discussion:

What is the theoretical value of the acceleration of the cart?

What is the experimental value of the acceleration extracted from the x(t) graph and v(t) graph? Compute the percentage error in each case

Conclusion

II

Free Fall Accelerated Motion

(Displacement and speed behavior as a function of time)

Purpose:

Introduction

Procedure:

Data

Time and vertical position readings from graph

Δt = 0.025 s (timer at 40 Hz)

 Point # t (s) y (m) Δy (m) v = Δy/Δt (m/s) 1 0.025 0 0 0 2 0.050 2.7 2.7 54 3 0.075 5.8 3.1 41 4 0.100 9.6 3.8 38 5 0.125 13.9 4.3 34.4 6 0.150 18.7 4.8 32 7 0.175 24.2 5.5 31.4 8 0.200 30.2 6 30 9 0.225 36.8 6.6 29.3 10 0.250 43.8 7 28

Analysis and discussion:

Studying the position during free fall motion y = y0 + v0.t + ½ g.t2

· Plot y vs. t (y on the vertical axis and t on the x-axis) using Excel.

· Use the fitting tool on Excel to fit your scattered data points into a second order polynomial.

· Use the result of the fitting equation to find the experimental acceleration of gravity.

· Compare the calculated value of g to the accepted value and calculate the percentage error.

Studying the speed during free fall motion v = v0 + g.t

· Plot v vs. t (v on the vertical axis and t on the x-axis) using Excel.

· Use the fitting tool on Excel to fit your scattered data points into a linear fit (first order polynomial).

· Use the result of the fitting equation to find the experimental acceleration of gravity.

· Compare the calculated value of g to the accepted value and calculate the percentage error.

Conclusion

III

Free Fall Accelerated Motion

(Velocity behavior as a function of distance)

Purpose:

We will verify the velocity behavior as a function of distance for uniformly accelerated object

Introduction

If an object is free falling a distance y from rest (v0 = 0), then, the velocity as a function of falling distance y is given by

v2 = 2.g. y

Procedure:

Data

d = 1.5 cm ; v = 1.5 cm/ t(s)

 y (cm) t1 (s) t2 (s) t3 (s) tavg (s) y (cm1/2) v (cm/s) 10.0 0.01 0.01 0.01 0.01 3.16 1000 20.0 0.0074 0.0076 0.0073 0.0074 4.47 2702 30.0 0.0062 0.062 0.0064 0.0063 5.47 4761 40.0 0.0055 0.0059 0.0056 0.0056 6.32 7142 50.0 0.0051 0.0052 0.0052 0.0051 7.07 9803

Analysis and discussion:

Plot vs.

vy

, where v

is on the y-axis and y

on the x-axis. Fit your data points to a straight line. Compare the equation of the straight line you obtained from Excel:y = a.x + b

to Equation: =2g

vy

Extract an experimental value for g to judge the accuracy of your experiment.

Conclusion

IV

The acceleration of an Object on a frictionless incline

Purpose:

Introduction

When an object is pushed up a smooth inclined surface (or allowed to run down the smooth incline), it’s deceleration up the incline (acceleration down the incline) has a magnitude that is given by:

a = g . sinθ Eq. 1 Procedure:

Data

Object moving down the incline

 θO a (m/s2) a1 a2 a3 aavg 0 54.8 56.8 53 54.9 10 204 201.9 217.5 207.7 8 155.1 150.9 152.3 152.8 5 149.5 141.4 145.3 145.4 3 75.7 66.2 77.2 73

Analysis and discussion:

· Plot a vs. sin θ

· Fit your data points to a straight line.

· From the fitting equation you obtained using Excel, find the acceleration of gravity

Conclusion

Engineering/Physics Department