Ramp+Problems

One of the most common types of questions that show up on the AP test is the ramp problem. It can be used to test your knowledge of force, weight, acceleration and tension. [|FBD3b.jpg] There are five different types of forces as shown above. > F y - Force in the y direction. Fy = mgcosø > F g - Force of gravity; F g =mg. > > F t Force of tension. The problems usually have some of these variables missing and requires the test taker to solve for the remaining variables. =__**How to Draw a Ramp Diagram**__= 1. Draw a Right triangle. 2. Draw a box on the surface of the hypotenuse of the triangle. 3. Draw a vector straight down from the center of the box perpendicular to the horizontal axis to represent the Force of Weight. 4. Draw a Vector perpendicular to the surface of the ramp upwards. This is the Normal Force. 5. Draw a line parallel to the slope of the ramp starting from the tip of the Weight vector and connecting to the line of the force that is opposite of the Normal Force. This should now make a another right triangle that is similar to the ramp. 6. The line that was drawn parallel to the slope of the ramp has a magnitude equal to the Downhill force. 7. Draw a magnitude that represents the Downhill force starting from the box toards the end of the slope. 8. If applicable draw the Force of Friction in the opposite direction of the Downhill force. 9. Determine magnitude of forces through the use of trigonometry and with the Force of weight.
 * F x - Force in the x direction. F x = mgsinø
 * F n - Normal force, force that is always perpendicular to the ramp. F n =mgcosø
 * F f - Force of friction. [[image:http://upload.wikimedia.org/wikipedia/en/math/0/c/0/0c02725f116ef3cad99527413171d4bb.png width="55" height="12"]]
 * F=Ma


 * [[image:dffhfjftfj.jpg width="720" height="377"]]

=__**Steps To Solving a Ramp Problem**__=

Step 1: Identify
 * Make a list of all Known and Unknown Quantities
 * Choose the Equations to Solve the Problem
 * Identify Target Variable

Step 2: Set Up Problem
 * Summarize the Situation with a Ramp Diagram Diagram (Draw a Sketch)

Step 3: Execute
 * Do the Math / Work with Symbols
 * Be Neat and Organized / Keep it Simple

Step 4: Evaluate =__**EXAMPLES**__= Answers are shown below.
 * Dimensionally Consistent? Numbers with Units and reasonable Significant Figures
 * Ask Yourself: Does this Answer Make Sense?
 * __1.__** A 10.0 kg box accelerates at 2.00 m/s2 as it slides down a ramp that makes an angle of 25.0 degrees with the horizontal. Find the coefficient of friction.

__**2.**__ A box of unknown mass is accelerating down a 45 degree friction less ramp at a rate of 25 m/s2 and a force of 50 N. What is the mass of the box.

__**3**__. A block slides down an inclined plane that makes a 30 degree angle with the horizontal. If the coefficient of kinetic friction is 0.3 what is the acceleration of the block?


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 * __1.__** A 10.0 kg box accelerates at 2.00 m/s2 as it slides down a ramp that makes an angle of 25.0 degrees with the horizontal. Find the coefficient of friction.

Target = coefficient of friction.

You will need F=ma,, F x = mgsinø, F n =mgcosø

Known ø= 25.0 degrees a= 2.00 m/s 2 m= 10 kg g= 10m/s 2

Unknown F n =? F f =? F x =? μ=?

Fd= 10kg*2m/s 2 = 20N Fx= 10kg*10m/s2*(sin25)= 42.26N Ff= Fx - Fd = 42.26N-20N= 22.26N Fn=10kg * 10m/s 2 * cos(25)= 90.63N Ff=22.26N=μ*Fn= μ*90.63N μ= 22.26N/90.63N= 0.2456 Coefficient of friction is 0.2456.

__**2.**__ A box of unknown mass is accelerating down a 45 degree friction less ramp at a rate of 25 m/s2 and a force of 50 N. What is the mass of the box.

Target= mass You need F d =mgcosø

Fd =mgsinø Knownø= 45.0 degrees a= 25.00 m/s2 g= 10m/s2 Fd= 50N Unknown m=?

Fd= 50N = mgcosø= m * 10m/s2 * cos 45 degrees = m*7.0711m/s2 m= 50N/7.70711m/s2= 6.4851 kg Mass is 6.4851 kg.

__**3**__. A block slides down an inclined plane that makes a 30 degree angle with the horizontal. If the coefficient of kinetic friction is 0.3 what is the acceleration of the block?

Target= acceleration

You need Fd=mgcosø, Fn=mgsinø, Ff=uFn.

Known ø=30 degrees u=0.3 g=10m/s2

Unknown Fd=? Fn=? Ff=? m=?

Fd=mgsinø - umgcosø= mg(sinø-ucosø) a=Fd/m= mg(sinø-ucosø)/m=g(sinø-ucosø)= (10m/s2)(sin30degrees - 0.3cos30degrees) = 2.4m/s2 Acceleration is 2.4m/s2.