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Gravity of It All
I LOVE Science
November
Gravity of It All activity
Explore momentum of a marble rolling down a ramp and transfer of momentum to a cup
Kit contents: grooved metric ruler, washer, tape, marble, small paper/plastic cup (cut in half), measuring tape, 3
books (use science books)
Key concepts: force, friction, gravity, balanced forces, unbalanced forces
Science Standards:
The student knows that the motion of an object is determined by the overall effect of all of the forces acting on the
object (SC.C.2.2.4)
The student knows that it is important to keep accurate records and descriptions to provide information and clues on
causes of discrepancies in repeated experiments (SC.H.1.2.1).
The student knows that a successful method to explore the natural world is to observe and record, and then analyze
and communicate the results (SC.H.1.2.2).
Basic Procedure
1.
Assemble ruler ramp using 3 books and one ruler. Place the cup with the open end covering the bottom of the
ruler so that the ball will collide with the bottom of the cup. Tape a washer to the top of the cup to add mass.
(Optional)
2. Ask students, “What will happen when the marble rolls down the ramp and hits the cup?” “What if you used a
different height?” Discuss how the marble is the controlled variable in the experiment.
3. Release marble to go down the ramp. Measure the distance the cup travels. Record the distance in
centimeters on table.
4. Have students repeat the experiment two more times for accuracy.
5. Using two books, repeat experiment.
6. Repeat using one book.
7. Ask students, “What force(s) were acting on the ball as it was rolling down the ramp?” “Does the height affect
the distance the cup moved?”
8. Discuss with students the controlled variables in this experiment (type of ball, surface, the way the ball was
released, ruler), the independent variable (i.e., the variable the experimenter changed: height of books), and
the dependent variable (i.e., the value that changed due to the change in the independent variable: distance
the cup moved).
9. Ask, “Why is it important to repeat trials?
10. Students can make a graph to go with data table.
Science Background
This experiment has two different scientific ideas--the acceleration of the marble due to gravity and the transfer of the
marble's momentum to the cup. (Additionally, the idea of friction is important as to why the cup stops.)
Falling bodies
Galileo is one of the most famous scientist to investigate falling bodies. He used a similar experiment to demonstrate
the the acceleration of gravity is a constant. Until Galileo, people believed the Aristotlean ideas that there are two
kinds of motion, unnatural and natural. Unnatural is when an object is being pushed by an outside object. Natural
motion is the motion of a body as it reaches its natural place in the universe. Aristotle declared that the speed of a fall
was proportional to weight.
Galileo's experiments demonstrated that the speed of a fall is constant, regardless of weight, at least on Earth.
Gravity on Earth is a constant acceleration toward Earth. In this experiment, however, the acceleration of the marble
is different based on the angle of the ramp. In truth, the acceleration is g*sin θ, where g is the acceleration due to
gravity and θ is the angle of the ramp, since the marble is not able to travel straight down. This explains why the
marble will not roll when the angle is too small.
Velocity of marble vs. velocity of cup
The velocity of the marble is simply dependent on the change from potential to kinetic energy; that is, the potential
2
energy at the top (mgh) must equal the kinetic energy at the bottom (1/2 mv ). The transfer of the velocity of the ball
to the velocity of the cup/ball (since the ball comes along with the cup) is dependent on the conservation of
momentum; that is, m1v1=m2v2 . With a sufficiently large ball, the weight of the cup is much less than the weight of the
ball, so the masses cancel out, leaving just velocity.. Velocity, however, is a vector, so the angle of the velocity is
important to consider. Instinct tells us that, if the ball is dropped straight down, it will bounce, not hitting the cup, and
therefore not transfer any momentum to the cup. In this case, we must consider that the angle of the ramp affects the
Gravity of It All
I LOVE Science
November
transfer of momentum by the cos θ . Because of the effect of the angle on the acceleration due to gravity (sin θ) and
the effect of the angle on the transfer of momentum (cos θ ), the height at which the cup should travel farthest should
be 45 degrees (discounting friction).
Some assumptions in the above description, such as the inelasticity of the collision or the relative weights of the ball
and cup, can cause complications in the experiment. For instance, the ball doesn't completely stick to the cup but
actually can bounce back toward the ruler or will travel in the same direction but not with the cup. These situations
make the conservation of momentum become mballvramp=mballvdesk +mcupvcup which gets more and more complicated to
solve.
Force Diagram and equations
The diagram below shows the set up of this experiment. At point a, the ball is ready to be released; at b it has
reached the lowest point on the ruler; and at c the ball and cup have come to a complete stop. When the ball is
initially released, the forces acting on the ball are the force of gravity pulling it down and the force of the ruler
constraining it to travel at an angle (this is referred to as the "normal force"). The acceleration on the ball in the
direction it can travel is m*g*sinθ. There is also a force of friction which opposes the motion. At point b, the only
forces acting on the ball are the force of gravity and the force of the table which cancel each other out. As the ball
moves from b to c, the only force that isn't balanced is the force of friction, in the opposite direction than that of travel.
What does all of this tell us about what to expect about the relationships between height released and distance
2
traveled? At point a, the energy is mgh. At b, the energy is 1/2 m*v . At point c, the energy of the ball is 0. Between b
and c, the energy loss is equal to m*α*d, where α is the acceleration of friction, and d is the distance traveled. Using
the conservation of energy, the energy at point a should equal the energy lost getting to point c, so mgh= m*α*d, so
height should equal α*d/g. This shows that the mass is irrelevant. This is a bit of a simplification, since it leaves out
the friction of the ramp/ruler. However, if the friction of the ball on the ruler is similar to the cup on the table, then the d
should be the sum of the distance between a and b and b and c. Also, the ability to cancel out mass relies on the cup
being insignificant compared to the ball. All of this clauses are variables that the students can test.
Common Misconceptions about Motion
Most people's instinct is Aristoliean--everything they see in motion eventually stops moving. By allowing the students
to explore the effects of different materials' friction, the better able they will comprehend what might happen if friction
is completely absent.
Students also need to develop their abilities in describing motion. Acceleration and velocity are often confused.
Gravity causes a constant acceleration, resulting, initially, in an increasing velocity.
Student also believe that there cannot be a force without motion and if there is no motion, then there is no force
acting. The idea of balanced forces is challenging.
Script Idea
What we will learn about today--Motion, gravity and acceleration!!
What do the students know about motion? What words do they know that relate to motion (direction, velocity/speed,
acceleration). What causes motion (forces)? Do all forces cause motion? (they likely have covered the concept of
balanced and unbalanced forces)
Demonstrate the basic activity, the marble rolling down the ramp and hitting the cup. Can the students describe the
motion they saw? Try to get them to include words like speeding up, slowing down, not just that the ball rolled
What forces were acting in the demo? Which were balanced and unbalanced forces? They could include your hand
holding/moving the marble, gravity on the marble, friction on the marble, gravity on the cup, friction on the cup. The
hand holding the marble in place at the beginning is a balanced force, but when the marble is released there is an
unbalanced force.
Gravity of It All
I LOVE Science
November
What are some variables that you could change in this experiment? List them on the board as the students say them,
include others if they are unable to think of enough. Then let the groups choose one variable to investigate.
•
•
•
•
•
•
height of start of marble
angle of ramp
surface marble rolls down (you may want to have the marble roll between two rulers on different surfaces,
like cloth vs a book)
weight of marble (you will need to bring an extra marble--try to have a similar diameter)
weight of cup (tape weights (coins, etc) to the inside
surface cup travels on (perhaps compare the desk with the floor (if it is carpeted) or put the cup on a cloth or
other higher friction thing)
Make sure the students clearly state their hypothesis--what result they expect. Also have them note the variables they
are going to change and which they will hold constant. Challenge students to try to keep as many variables constant
as possible. For example, if they change the height of the ball release, they can either change it by releasing it further
up or down the ruler with the same angle, but that will change the distance it rolls on the ruler, or they can change the
angle but release the ball at approximately the same height.
Have the students report back to the class the results of their experiments. Ensure that they provide as much detail
as they can and encourage the rest of the class to ask questions. Perhaps challenge the rest of the class to say
which variables were changed as a way to maintain their attention. This is a great activity for graphing--do different
weight marbles have similar curves of height of drop vs. distance cup goes, etc. Encourage groups to create a rough
graph to share with the rest of the class.
To conclude, have students discuss which variables had the most effect on the experiment. Additionally, you may
want them to work as a large group to plot how the angle of the ruler affects the distance the cup travels.
Key Knowledge
Vocabulary
force - a push or a pull that causes changes in motion
friction - a force that works against motion
gravity - force of attraction between an object and Earth
balanced forces - forces that act on an object but cancel each other
unbalanced forces - forces that act on an object and cause a change in motion
position - location of an object in space
speed - distance an object travels in a certain amount of time
velocity - measure of an object's speed in a particular direction
acceleration - rate at which velocity changes
momentum - how hard it is to slow down or stop an object, momentum = mass x velocity
Concepts
Conservation of momentum: Momentum is the mass of an object multiplied by the velocity of the object. The
conservation of momentum states that the amount of momentum in a system (not necessarily in a single object)
remains constant. For example, if to billiard balls collide, the momentum of both balls will change, but the momentum
of the system will remain constant. Momentum is neither created nor destroyed, but only changed through the action
of forces as described by Newton's laws of motion. Dealing with momentum is more difficult than dealing with mass
and energy because momentum is a vector quantity having both a magnitude and a direction.
Measurement of motion. A given object's motion can be described in several ways. Its velocity is the current motion,
and the acceleration is the rate of change of velocity. The acceleration is due to an unbalanced force. There can also
be balanced forces acting on that object. For example, an object sliding across a frictionless surface on the ground,
similar to a sheet of ice, is being acted on by gravity but gravity is not causing any acceleration. If an object is
travelling at constant velocity, there are no unbalanced forces (in a frictionless world).
Newton's first law: No acceleration can happen without a force. An object at rest tends to stay at rest; an object in
motion tends to stay in motion
Newton's second law: An object's acceleration depends on the object's mass and the force applied to it. Force =
mass x acceleration
Newton's third law: Whenever one object applies a force to a second object, the second object applies an equal and
opposite force to the first object.
Gravity of It All
I LOVE Science
November
Alternate Ideas
Projectile Motion
One challenge with the experiment as described is that there are a number of forces and principles (two frictions,
conservation of momentum, whether the collision with the cup is elastic or inelastic, whether the mass of the cup is
negligible or significant). An alternate idea is to change the experiment to be projectile motion.
Galileo
The experimental set up used is very similar to that used by Galileo in his studies of gravity. However, instead of
having the ball hit a cup, he timed the ball rolling down the ramp from multiple points. It might be easiest to emulate
the Galileo experiments with a long ramp, perhaps two meter sticks on a board or such. A graph of time vs. starting
point should show an approximate quadratic curve. The approximate equation the kids could understand is that it is
d=c*t*t, where d is distance and t is time. c is a constant for a given height, equaling 1/2 a*sin q, where a is the
acceleration of gravity and q is the angle of the ramp. These kids don't know trigonometry or even algebra yet, but if
they plot the distance vs. time at various heights, they will see that there is some effect of the angle. There is
information on the actual experiment at http://galileo.phys.virginia.edu/classes/109N/lectures/gal_accn96.htm.
Straw through the Potato
The straw through the potato demo shows how velocity is a component of momentum, how a light, weak object can
have a strong effect if travelling at high speed. For more information on momentum, explore the momentum crash
test information.
Straw through Potato
If a plastic straw (like those from McDonald's) is pushed slowly into a raw potato, the rigid potato will cause the softer
plastic straw to bend and break. However, if a significant velocity is given to the straw it can be pushed clean through
the potato. This is what often happens in a tornado, where apparently softer objects are accelerated to high speeds
by the wind and driven through apparently harder objects.
What is happening: A straw moving slowly has less momentum, and less force is necessary to stop it, so the potato
just stops it. A fast moving straw has more momentum, and therefore more force is necessary to stop it. That
stopping force is large enough to break the skin of the potato and penetrate the straw through the potato.
Projectile motion
What we will learn about today--Motion, gravity and acceleration!!
What do the students know about motion? What words do they know that relate to motion (direction, velocity/speed,
acceleration). What causes motion (forces)? Do all forces cause motion? (they likely have covered the concept of
balanced and unbalanced forces)
Assemble ruler ramp using 3 books and one ruler. Have the end of the ruler about a centimeter from the end of the
desk. Place a cookie sheet/jelly roll pan or other tray with sand (could use carbon paper or even just newsprint and
look for the impact) on the floor.
Ask the students what path they think the marble will travel. Demonstrate the experiment by letting the marble roll
down the ramp and put a divot in the sand. Can the students describe the motion they saw? Try to get them to
include words like speeding up, slowing down, not just that the ball rolled
What forces were acting in the demo? Which were balanced and unbalanced forces? They could include your hand
holding/moving the marble, gravity on the marble, friction on the marble. Try to get them to separate their discussion
of the forces into the two parts, the marble on the ramp and the marble flying through the air. The hand holding the
marble in place at the beginning is a balanced force, but when the marble is released there is an unbalanced force.
What are some variables that you could change in this experiment? What can the students measure in the
experiment? List the variables they can change on the board as the students say them, include others if they are
unable to think of enough. Then let the groups choose one variable to investigate.
•
•
•
•
height of start of marble
angle of ramp
surface marble rolls down (you may want to have the marble roll between two rulers on different surfaces,
like cloth vs a book)
weight of marble (you will need to bring an extra marble--try to have a similar diameter)
Gravity of It All
I LOVE Science
November
Make sure the students clearly state their hypothesis--what result they expect. Also have them note the variables they
are going to change and which they will hold constant. Challenge students to try to keep as many variables constant
as possible. For example, if they change the height of the ball release, they can either change it by releasing it further
up or down the ruler with the same angle, but that will change the distance it rolls on the ruler, or they can change the
angle but release the ball at approximately the same height.
They should measure the distance the marble travels from the end of the desk and do several trials for each change
in the vaiable.
Have the students report back to the class the results of their experiments. Ensure that they provide as much detail
as they can and encourage the rest of the class to ask questions. Perhaps challenge the rest of the class to say
which variables were changed as a way to maintain their attention. This is a great activity for graphing--do different
weight marbles have similar curves of height of drop vs. distance cup goes, etc. Encourage groups to create a rough
graph to share with the rest of the class.
To conclude, have students discuss which variables had the most effect on the experiment.
Background: Once the ball leaves the table, the acceleration due to gravity is the only acceleration. Therefore, the
time it takes the ball to land on the ground is constant with different heights. The velocity perpendicular to the ground
is the only thing changing. Remind them that velocity is distance/time, so in this experiment, distance is a constant
times velocity. Thus with this we can compare how the velocity of the ball at the bottom of the ramp relates to the
height of the ramp. Based on conservation of energy, at the top of the ramp, the ball has mgh and at the bottom it is
1/2 mv2. They should then be able to graph a parabolic curve relating height to velocity (distance). In addition, they
could discover that mass is not a factor, assuming the friction of the ball rolling down the ramp isn't too large.
There are two ways to change the height of the ball release in this experiment. One is to put the ball at a different
point on the ruler, keeping the slope the same. If, instead, they change the slope, the component of velocity
perpendicular to gravity will change and that can become a factor in the experiment. (If it is too steep, the ball will
bounce off the table.
Another option is to look at the vertical drop by having the ramp aim for a wall, moving it back incremental distances.
Students should see the exponential speed of the drop.