Making the grade

Preliminary Question:

A. Suppose that a car traveled up three different roadways (each with varying incline angle or slope) from the base of a mountain to the summit of the mountain. Which path would require the most gasoline (or energy)? Would the steepest path (path AD) require the most gasoline or would the least steep path (path BD) require the most gasoline? Or would each path require the same amount of gasoline?

Include discussion/introduction Data table height Example calculation of work to pull up ramp Example calculation of work to lift.

Background from the physicsclassroom.com

Formulas:

Work = Force * distance, W = F*d , Units: Work [Joules] = F [Newton]* d [meter]

Efficiency = Work _{(up ramp)} / Work _{(to lift)}

Data Table sample:

Height =

F_g, Weight of cart =

	25o	35o	45o	60o
Force
Distance
Work (up ramp) W = F * d
Work (to lift) W = Fg * h
Efficiency

Procedure:

Variables: F, the force you needed to pull the cart up the ramp. [Newtons] d, the distance you pulled the cart up the ramp. [meters] h, The vertical height the cart moves as a result of being pulled up the ramp, i.e. vertical measurment from the back of the cart to the back of the cart after it is pulled up the ramp.[meters]

To find the total energy gained by the work do in lifting the cart to the height of you lab table.

Work = F * d * cos(o)

1. F = Measure the Force to lift, F_g by suspending the cart from the spring scale.

2. d = the vertical height of the lab table.

3. angle is zero, so cos 0^o is 1

To collect the data.

1. Set up the lab material; ramp, cart, green spring scale

• Lean the ramp on the lab table to set it to your first angle of 25^o. Position the protractor so that the bullet is aligned with the bottom side of the track.
• 

 

2. Pull the cart up the ramp using the spring scale, be sure to pull parallel to the ramp, record the force, F, in the data table. (You may also just hold the cart on the track and read the scale.)

This is the actual force up the ramp and is in the direction of the displacement! You don't need to use the cos(o) in the work formula.

3. Measure, distance, d, that you pulled the cart along the ramp. record this in the data table

4. Change the angle of the ramp without changing the vertical height. This means that the distance, d, will change as the angle changes. Be sure to secure the new ramp location by placing two bricks at the end of the ramp and sliding the ramp foot against the lab table top. Have on lab partner "spot" the ramp at all times. Collect a new data set.

 

Analysis:

1. What pattern or relationship do you find between the forces and the distances as you change the angle of the incline? Support your answer with citations from your data and analysis. This is the most important question - spend the most time on it.
2. Does it take more or less force to move the cart using the incline plane? Support your answer with citations from your data and analysis.
3. Does it take more or less work to move the cart using the incline plane as compaired to the work lifting the cart directly? Support your answer with citations from your data and analysis.
4. What causes the difference between the work needed to pull the cart up the incline and the work needed to lift it to the same height? Discuss ways to decrease this difference.
5. Design an experiment to study your answer to question 4.