Calculating Time it Takes for Soap to Slide Down a Ramp

In summary, a wet bar of soap slides down a 9.35 m long ramp inclined at 7.00° with a coefficient of friction of 0.0550. To determine the time it takes to reach the bottom, a free-body diagram and Newton's 2nd law can be used to solve for the acceleration. The mass of the soap is not needed as it is a common factor that can be eliminated in the equations.
  • #1
strugglin-physics
47
0
A wet bar of soap slides freely down a ramp 9.35 m long inclined at 7.00°. How long does it take to reach the bottom? Assume muk = 0.0550.

Okay I've got my x & y componants
9.35cos(7)=9.28
9.35sin(7)=1.14

But now what since I don't have the mass of the soap or the acceleration, what do I do next?
 
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  • #2
Draw yourself a free-body diagram of the situation. It should be pretty clear to you from then on.
 
  • #3
Okay I drew my FBD but I still don't know how much time it would take the soap to slide down the ramp. Maybe I'm missing something.
I have the frictional force going NW the normal force going NE and the weight force going South... is that right?
 
  • #4
Yes. Set up the equations using Newton's 2. law, solve for the acceleration and use some kinematics to solve for time.
 
  • #5
How do I solve for acceleration if the mass is unknown?
 
  • #6
Well, but since the frictional force, the gravity and the "ma" terms are all proportional to the mass, it's a common factor which you can eliminate
(the solution is independent of the mass)
 

1. How do you calculate the time it takes for soap to slide down a ramp?

The time it takes for soap to slide down a ramp can be calculated by using the formula t = √(2h/g), where t is the time in seconds, h is the height of the ramp in meters, and g is the acceleration due to gravity (9.8 m/s²).

2. Does the mass of the soap affect the time it takes to slide down the ramp?

No, the mass of the soap does not affect the time it takes to slide down the ramp. This is because the formula only takes into account the height of the ramp and the acceleration due to gravity, which are both constant regardless of the mass of the object.

3. How do you measure the height of the ramp?

The height of the ramp can be measured using a ruler or measuring tape. Place one end of the ruler at the base of the ramp and measure vertically to the top of the ramp.

4. Is air resistance taken into account when calculating the time for soap to slide down a ramp?

No, the formula for calculating the time does not take into account air resistance. However, in real-world situations, air resistance can affect the time it takes for the soap to slide down the ramp.

5. Can this formula be used for objects other than soap?

Yes, this formula can be used for any object sliding down a ramp as long as the height and acceleration due to gravity are known. However, for objects with different shapes or sizes, air resistance and other external factors may need to be taken into consideration.

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