Lab Ramps: Sliding vs Rolling
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

Background

Remember that when analyzing two-dimensional 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 = vHt, where vH 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 vo = 0, a = -9.8 m/sec2, and s = -h and then used the kinematics equation  s = vot + ½at2 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's-eye 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.

 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/sec2) 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). PEtop = KEbasemgh =  ½mv22mgh =  mv2√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's-eye 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's-eye.   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 vH at the base of the ramp.           vH (in m/sec) =

 Step 9: Using your original experimental range and the actual vH 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.

 trialdescription total distancefallen flight time(sec) vertical vf(m/sec) actual vH(m/sec) resultantimpact velocity
 table top
 elevated release

 trialdescription total height(include ramp) total PE(at start) total KE(at impact) Energylost
 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

KErot = (1/5)mv2.

Notice that KErot, 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.