Calculating Motion on a Ramp Without Mass

In summary, the problem involves a train traveling up a 5.0 degree incline at a speed of 2.55 m/s. The last car breaks free and begins to coast without friction. The task is to determine how long it will coast before stopping momentarily. The equation F=mg or F=ma can be used to calculate the acceleration and solve for the time. However, without a given mass, the task becomes more challenging. One solution is to use the component of gravitational acceleration pointing down the ramp, without the need for force calculations.
  • #1
BraedenP
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0

Homework Statement


A train is traveling up a 5.0 degree incline at a speed of 2.55 m/s when the last car breaks free and begins to coast without friction. How long does it coast before stopping momentarily?


Homework Equations


[tex]F=mg[/tex] or [tex]F=ma[/tex] more generally.


The Attempt at a Solution


I would normally use the object's mass to find a vertical force of gravity, and then use the degree of incline to find the force directed down the ramp, with which I could calculate acceleration and solve for the time.

However, without a given mass, I'm stuck..

How do I find a force (or is there a straight way to get the acceleration?)
 
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  • #2
1. F(net) does not equal mg in this situation.
2. Draw your sum of forces, and work out the algebra. Mass eventually cancels out.
 
  • #3
thrill3rnit3 said:
1. F(net) does not equal mg in this situation.
2. Draw your sum of forces, and work out the algebra. Mass eventually cancels out.

Oh duh! I'm so retarded sometimes.. All I needed to do was work out the component of gravitational acceleration pointing down the ramp. No force calculations required at all.

Thanks! :P
 
Last edited:

1. How do you calculate the acceleration on a ramp without mass?

The acceleration on a ramp without mass is calculated by dividing the net force acting on the object by its mass. This can be represented by the equation a = F/m, where a is the acceleration, F is the net force, and m is the mass. On a ramp, the net force is equal to the component of the force of gravity that is parallel to the ramp's surface.

2. What is the formula for calculating the angle of a ramp?

The formula for calculating the angle of a ramp is given by the equation θ = tan⁻¹(h/l), where θ is the angle of the ramp, h is the height of the ramp, and l is the length of the ramp. This equation can be derived from the trigonometric function tangent, which is defined as the ratio of the opposite side (height) to the adjacent side (length) of a right triangle.

3. How does the angle of a ramp affect the motion of an object?

The angle of a ramp affects the motion of an object by determining the amount of force required to move the object up or down the ramp. A steeper angle will require more force to overcome the force of gravity, resulting in a higher acceleration. On the other hand, a shallower angle will require less force and result in a lower acceleration. Additionally, a steeper angle will result in a longer distance traveled, while a shallower angle will result in a shorter distance traveled.

4. Can you calculate the speed of an object on a ramp without mass?

Yes, the speed of an object on a ramp without mass can be calculated using the equation v = √2gh, where v is the speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the ramp. This equation is derived from the principle of conservation of energy, which states that the total energy of a system remains constant. In this case, the potential energy gained by the object as it moves up the ramp is converted into kinetic energy, which can be represented by the formula ½mv².

5. How does friction affect the motion of an object on a ramp without mass?

Friction can affect the motion of an object on a ramp without mass by slowing down its movement. Friction is a force that opposes the motion of an object and is caused by the interaction of surfaces. On a ramp, friction can be present between the object and the ramp's surface, as well as between the ramp and the ground. This force can reduce the acceleration of the object and cause it to move at a slower speed. To accurately calculate the motion on a ramp, the effects of friction must be taken into account.

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