Calculating Speed on an Inclined Plane | Mechanical Energy #2

In summary, a 19 kg box sliding down a 4.5 m frictionless ramp from a height of 1.3 m will have a velocity of the square root of 2 x 9.8 x 1.3 m/s at the bottom of the ramp, assuming conservation of mechanical energy and using the formulas for potential and kinetic energy.
  • #1
billyghost
5
0
A 19 kg box starts at rest and slides down a frictionless ramp. The length of the ramp is 4.5 m and the height above the ground at the top is 1.3 m. How fast is the box moving at the bottom of the ramp?

Unsure of inclined planes...help with formulas, etc.?
 
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  • #2
Think conservation of mechanical energy (KE + PE). (Measure the potential energy from the bottom of the ramp.)

Mechanical Energy (at top of ramp) = Mechanical Energy (at bottom of ramp)
 
  • #3
19 x 1.3 x 9.8 ?
 
  • #4
billyghost said:
19 x 1.3 x 9.8 ?
That looks like a calculation of the PE at the top of the ramp: PE = mgh. (The units will be Joules.) Which happens to be the total mechanical energy, since it starts from rest. Since energy is conserved, this also equals the KE at the bottom of the ramp. ([itex]{KE} = 1/2 m v^2[/itex])

So set the PE at the top (mgh) equal to the KE at the bottom ([itex]1/2 m v^2[/itex]) and solve for the speed.
 
  • #5
Therefore,velocity should be the square root of 2 x 9.8 x 1.3
 
  • #6
Right. But be sure to give your answer with the proper units.
 

1. How do you calculate the speed of an object on an inclined plane?

The speed of an object on an inclined plane can be calculated using the formula: speed = √(2ghsinθ), where g is the acceleration due to gravity, h is the height of the object on the inclined plane, and θ is the angle of the inclined plane.

2. What is the relationship between mechanical energy and speed on an inclined plane?

Mechanical energy and speed on an inclined plane are directly proportional. This means that as the speed of the object on the inclined plane increases, its mechanical energy also increases. This relationship is described by the formula: mechanical energy = ½mv², where m is the mass of the object and v is its speed.

3. Can you calculate the speed on an inclined plane without knowing its angle?

Yes, the speed on an inclined plane can also be calculated using the formula: speed = √(2gh), where g is the acceleration due to gravity and h is the height of the object on the inclined plane. This formula does not require knowledge of the angle of the inclined plane.

4. How does friction affect the speed of an object on an inclined plane?

Friction can slow down the speed of an object on an inclined plane by converting some of its mechanical energy into heat energy. This means that the speed of the object will gradually decrease as it moves along the inclined plane due to the force of friction acting against it.

5. What are the units used to measure speed on an inclined plane?

Speed on an inclined plane is typically measured in meters per second (m/s) or kilometers per hour (km/h). However, any unit of length divided by a unit of time can be used to measure speed on an inclined plane.

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