Lab
Ramps: Sliding vs Rolling
Printer Friendly Version
Purpose:
To determine whether an object that rolls down a ramp has the same range as an object which slides down a ramp.
Equipment needed:
Each group needs: ramp, steel ball, target paper, meter stick, plumb line
Resource Lessons:
2D projectiles (horizontal release)
,
Conservation of Energy
.
Background
Remember that when analyzing twodimensional projectile motion, the horizontal and vertical motions are independent of each other. Horizontally, projectiles in freefall travel at a constant velocity; while vertically, they experience uniform acceleration resulting in a classic parabolic trajectory. Our secret to working projectile problems was to build a chart in which we delineated the
Horizontal

Vertical
properties in each situation.
Horizontally, the only equation available to us was R = v
_{H}
t, where v
_{H}
represents the projectile's constant horizontal velocity. Vertically, in the above illustration, the projectile's initial velocity equaled zero, since it was launched straight forward. Usually, in this situation, we let v
_{o}
= 0, a = 9.8 m/sec
^{2}
, and s = h and then used the kinematics equation s = v
_{o}
t + ½at
^{2}
to solve for the time that the projectile spent in the air.
Your goal in this experiment is to predict where a steel ball will land on the floor after having rolled down an incline plane. The final test of your measurements and computations will be to position a bull'seye on the floor so that the ball lands in its center circle on the first attempt. Make sure that ALL measurements and calculations are reported with
three significant figures
.
Phase I: Calibrating Your Ramp
Step 1:
Assemble your ramp. Make it as sturdy as possible so the steel ball rolls smoothly and consistently. The ramp should not sway or bend. Since the ball must leave the table horizontally, make sure that the horizontal part of the ramp is level with the surface of the table. The vertical height, h, of the ramp should be no less than 7 cm.
Step 2:
Calculate the ball's horizontal velocity at the base of the ramp using conservation of energy principles. At the top of the ramp, if the ball is released from rest, it will only have potential energy, PE, which equals the product of its mass (in kilograms) times the acceleration due to gravity (9.8 m/sec
^{2}
) and its height (in meters) above an arbitrary reference line. At the base of the ramp, the ball has translational kinetic energy, KE, which equals half the product of its mass (in kilograms) times the square of its velocity (in m/sec).
PE
_{top}
= KE
_{base}
mgh = ½mv
^{2}
2mgh = mv
^{2}
√2gh = v
This velocity at the base of the incline will remain the ball's horizontal velocity when it leaves the table. Remember that you will need to consistently release the ball from the same height on the ramp as well as not put any pressure against the ramp that might result in it "springing" forward when the ball is released.
How high (in cm) was the back of your ramp (ruler) above the top of the table?
Show your calculations for the ball's horizontal velocity in the space provided below on your answer sheet. What will be your ball's horizontal velocity (in m/sec) at the base of its ramp (ruler)?
Why did you not need to measure the ball's mass?
Step 3:
Using a plumb line, string, and meter stick measure and record here the vertical height of the lab table above the floor. Height of table (in cm) =
Step 4:
Using the appropriate equation from the background information given above, calculate the time, t, that the ball will take to fall from the base of the ramp on the table's surface to the floor.
t (in sec) =
Step 5:
The range is the horizontal distance a projectile once it is leaves the table until it strikes the floor. Calculate the range of the ball. Show your equation and any necessary calculations used in predicting the ball's range.
R (in m) =
Teacher certification that you have calculated your experimental range.
Step 6
: Now tape the center of the bull'seye on the floor where you predict that the ball will strike. When you are ready to release your ball, call your instructor over to witness your trial. Remember to make sure that the ball is released from the top of the ramp. Leaving the target paper taped to the floor, measure how far the ball struck from the center of the bull'seye.
End of Phase I:
Our ball missed the center of the bullseye by ___ cm.
Phase II: Reaching the bullseye
Step 7:
Leaving the target paper in it's original location, measure the ball's actual range.
actual range: R (in m) =
Step 8:
Using your actual range and the actual time it spent in the air, calculate the ball's actual v
_{H}
at the base of the ramp.
v
_{H}
(in m/sec) =
Step 9:
Using your original experimental range and the actual v
_{H}
found in the previous question, calculate the time needed in the air for the projectile to reach the bullseye.
t (in sec) =
Step 10:
How high should the base of the incline be placed above the floor to insure that the ball will have sufficient time to reach the bullseye?
height (in m) =
Teacher certification that you have calculated your new height.
Step 11.
After making the adjustments outlined above, call your instructor over to witness a second release of your ball.
End of Phase II:
Our ball came within ___ cm of hitting the center of the bullseye!
Analysis
To continue with your analysis, you must obtain the mass of your marble.
Step 12.
State the mass of your marble in kg.
trial
description
total distance
fallen
flight time
(sec)
vertical v
_{f}
(m/sec)
actual v
_{H}
(m/sec)
resultant
impact velocity
table top
elevated release
trial
description
total height
(include ramp)
total PE
(at start)
total KE
(at impact)
Energy
lost
table top
elevated release
Step 13.
What is the percent difference between the two amounts of energy lost?
A form of energy that all rotating objects possess is called
rotational kinetic energy
. The same way that massive objects resist translational acceleration, they also resist rotational acceleration. This type of resistance is known as
rotational inertia
and gives rise to an energy known as rotational kinetic energy.
The rotational kinetic energy of a uniform rolling sphere can be calculated using the formula
KE
_{rot}
= (1/5)mv
^{2}
.
Notice that KE
_{rot}
, as is true with all types of energies, is measured in joules.
Step 14.
Using the actual horizontal velocity measured in
Step 8
, calculate your marble's rotational kinetic energy as it left the ramp.
Step 15.
What percent of the ball's lost energy in your first trial can be accounted for by its rotational kinetic energy.
Step 16.
What other form(s) of energy could account for the rest of the energy lost?
After submitting your results, each group is to turn in your "bullseye target" and all of your analysis calculations.
Related Documents
Lab:
Labs 
A Battering Ram
Labs 
A Photoelectric Effect Analogy
Labs 
Acceleration Down an Inclined Plane
Labs 
Air Track Collisions
Labs 
Ballistic Pendulum
Labs 
Ballistic Pendulum: Muzzle Velocity
Labs 
Bouncing Steel Spheres
Labs 
Coefficient of Friction
Labs 
Collision Pendulum: Muzzle Velocity
Labs 
Conservation of Energy and Vertical Circles
Labs 
Conservation of Momentum
Labs 
Conservation of Momentum in TwoDimensions
Labs 
Cookie Sale Problem
Labs 
Flow Rates
Labs 
Freefall MiniLab: Reaction Times
Labs 
Freefall: Timing a Bouncing Ball
Labs 
Galileo Ramps
Labs 
Gravitational Field Strength
Labs 
Home to School
Labs 
Inelastic Collision  Velocity of a Softball
Labs 
InterState Map
Labs 
LAB: Ramps  Accelerated Motion
Labs 
LabPro: Newton's 2nd Law
Labs 
LabPro: Uniformly Accelerated Motion
Labs 
LooptheLoop
Labs 
Mass of a Rolling Cart
Labs 
Moment of Inertia of a Bicycle Wheel
Labs 
Monkey and the Hunter Animation
Labs 
Monkey and the Hunter Screen Captures
Labs 
Projectiles Released at an Angle
Labs 
Range of a Projectile
Labs 
Roller Coaster, Projectile Motion, and Energy
Labs 
Rotational Inertia
Labs 
Rube Goldberg Challenge
Labs 
Spring Carts
Labs 
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs 
Terminal Velocity
Labs 
Video LAB: A Gravitron
Labs 
Video Lab: Ball Bouncing Across a Stage
Labs 
Video LAB: Ball ReBounding From a Wall
Labs 
Video Lab: Blowdart Colliding with Cart
Labs 
Video Lab: Cart Push #2 and #3
Labs 
Video LAB: Circular Motion
Labs 
Video Lab: Falling Coffee Filters
Labs 
Video Lab: M&M Collides with Pop Can
Labs 
Video Lab: Marble Collides with Ballistic Pendulum
Labs 
Video Lab: TwoDimensional Projectile Motion
Resource Lesson:
RL 
Accelerated Motion: A Data Analysis Approach
RL 
Accelerated Motion: VelocityTime Graphs
RL 
Analyzing SVA Graph Combinations
RL 
APC: Work Notation
RL 
Average Velocity  A Calculus Approach
RL 
Chase Problems
RL 
Chase Problems: Projectiles
RL 
Comparing Constant Velocity Graphs of PositionTime & VelocityTime
RL 
Conservation of Energy and Springs
RL 
Constant Velocity: PositionTime Graphs
RL 
Constant Velocity: VelocityTime Graphs
RL 
Derivation of the Kinematics Equations for Uniformly Accelerated Motion
RL 
Derivatives: Instantaneous vs Average Velocities
RL 
Directions: Flash Cards
RL 
Energy Conservation in Simple Pendulums
RL 
Freefall: Horizontally Released Projectiles (2DMotion)
RL 
Freefall: Projectiles in 1Dimension
RL 
Freefall: Projectiles Released at an Angle (2DMotion)
RL 
Gravitational Energy Wells
RL 
Mechanical Energy
RL 
Momentum and Energy
RL 
Monkey and the Hunter
RL 
Potential Energy Functions
RL 
Principal of Least Action
RL 
Rotational Dynamics: Pivoting Rods
RL 
Rotational Kinetic Energy
RL 
Springs and Blocks
RL 
Summary: Graph Shapes for Constant Velocity
RL 
Summary: Graph Shapes for Uniformly Accelerated Motion
RL 
SVA: Slopes and Area Relationships
RL 
Symmetries in Physics
RL 
Tension Cases: Four Special Situations
RL 
Vector Resultants: Average Velocity
RL 
Work
RL 
Work and Energy
Review:
REV 
Test #1: APC Review Sheet
Worksheet:
APP 
Hackensack
APP 
The Baseball Game
APP 
The Big Mac
APP 
The Cemetary
APP 
The Golf Game
APP 
The Jogger
APP 
The Pepsi Challenge
APP 
The Pet Rock
APP 
The Pool Game
APP 
The Spring Phling
CP 
2D Projectiles
CP 
Conservation of Energy
CP 
Dropped From Rest
CP 
Freefall
CP 
Momentum and Energy
CP 
Momentum and Kinetic Energy
CP 
NonAccelerated and Accelerated Motion
CP 
Power Production
CP 
Satellites: Circular and Elliptical
CP 
Tossed Ball
CP 
Up and Down
CP 
Work and Energy
NT 
Average Speed
NT 
BackandForth
NT 
Cliffs
NT 
Crosswinds
NT 
Elliptical Orbits
NT 
Escape Velocity
NT 
Gravitation #2
NT 
Headwinds
NT 
Monkey Shooter
NT 
Pendulum
NT 
Projectile
NT 
Ramps
NT 
Satellite Positions
WS 
Accelerated Motion: Analyzing VelocityTime Graphs
WS 
Accelerated Motion: Graph Shape Patterns
WS 
Accelerated Motion: Practice with Data Analysis
WS 
Advanced Properties of Freely Falling Bodies #1
WS 
Advanced Properties of Freely Falling Bodies #2
WS 
Advanced Properties of Freely Falling Bodies #3
WS 
Average Speed and Average Velocity
WS 
Average Speed Drill
WS 
Charged Projectiles in Uniform Electric Fields
WS 
Chase Problems #1
WS 
Chase Problems #2
WS 
Chase Problems: Projectiles
WS 
Combining Kinematics and Dynamics
WS 
Constant Velocity: Converting Position and Velocity Graphs
WS 
Constant Velocity: PositionTime Graphs #1
WS 
Constant Velocity: PositionTime Graphs #2
WS 
Constant Velocity: PositionTime Graphs #3
WS 
Constant Velocity: VelocityTime Graphs #1
WS 
Constant Velocity: VelocityTime Graphs #2
WS 
Constant Velocity: VelocityTime Graphs #3
WS 
Converting st and vt Graphs
WS 
Energy Methods: More Practice with Projectiles
WS 
Energy Methods: Projectiles
WS 
Energy/Work Vocabulary
WS 
Force vs Displacement Graphs
WS 
Freefall #1
WS 
Freefall #2
WS 
Freefall #3
WS 
Freefall #3 (Honors)
WS 
Horizontally Released Projectiles #1
WS 
Horizontally Released Projectiles #2
WS 
Introduction to Springs
WS 
Kinematics Along With Work/Energy
WS 
Kinematics Equations #1
WS 
Kinematics Equations #2
WS 
Kinematics Equations #3: A Stop Light Story
WS 
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS 
PositionTime Graph "Story" Combinations
WS 
Potential Energy Functions
WS 
Practice: Momentum and Energy #1
WS 
Practice: Momentum and Energy #2
WS 
Practice: Vertical Circular Motion
WS 
Projectiles Released at an Angle
WS 
Rotational Kinetic Energy
WS 
Static Springs: The Basics
WS 
SVA Relationships #1
WS 
SVA Relationships #2
WS 
SVA Relationships #3
WS 
SVA Relationships #4
WS 
SVA Relationships #5
WS 
Work and Energy Practice: An Assortment of Situations
WS 
Work and Energy Practice: Forces at Angles
TB 
2A: Introduction to Motion
TB 
2B: Average Speed and Average Velocity
TB 
Antiderivatives and Kinematics Functions
TB 
Honors: Average Speed/Velocity
TB 
Kinematics Derivatives
TB 
Projectile Summary
TB 
Projectile Summary
TB 
Projectiles Mixed (Vertical and Horizontal Release)
TB 
Projectiles Released at an Angle
TB 
Set 3A: Projectiles
TB 
Work, Power, Kinetic Energy
PhysicsLAB
Copyright © 19972017
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton