Forces and Motion - Ramp Question

In summary, the problem involves a ramp with an angle of 30 degrees and a height of 10 m. The task is to find the initial speed of a mass at the bottom of the ramp, assuming it is frictionless, so that it just reaches the top of the ramp. The attempt at a solution involved using kinematics equations and Newton's second law, but the answer was ultimately found using energy conservation. For part 1, the initial speed is 14 m/s, and for part 2 with a coefficient of static friction of 0.200, the initial speed is 16.2 m/s.
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Homework Statement


There is a ramp, with an angle of 30 degrees. The height of the ramp is 10 m. There is a mass at the bottom of the ramp. Assuming the ramp is frictionless, determine the initial speed that the mass must have so that it just comes to rest at the top of the ramp.

Part 2 is to repeat with a coefficient of static friction of 0.200.

Homework Equations



I assume all kinematics equations and the use of Newton's law equations.


The Attempt at a Solution



I tried finding the x and y components of velocity by using the height (10m) as distance, v2 = 0m/s and acceleration as 9.8 m/s^2. However, I was not sure how that would work for the horizontal component. I attempted to find the acceleration using Newtons second law; ma = F - mgsin30, however that leaves me with two variables. I was able to get the answer for the first part by using the kinematics equation 2da = v2^2 - v1^2 and using d = 10m, v2 = 0m/s, a = -9.8m/s^2 however I do not know how that works.

The answer for part 1 is 14 m/s, the answer for part 2 is 16.2 m/s.
 
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  • #2
You can use energy conservation. It's the easiest way.
I don't really understand your attempt.
 
  • #3
^ It looks like its just mgh=(1/2)mΔv[itex]^{2}[/itex]
 

FAQ: Forces and Motion - Ramp Question

What is a ramp and how does it affect forces and motion?

A ramp is a tilted surface that allows objects to move up or down with less effort. It affects forces and motion by changing the direction and magnitude of an object's motion. The angle of the ramp determines how much force is needed to move an object and the direction in which the object will move.

What is the relationship between the angle of the ramp and the force needed to move an object?

The steeper the angle of the ramp, the more force is needed to move an object up the ramp. This is because the steeper angle increases the component of the force needed to overcome gravity. On the other hand, a shallower angle requires less force as the component of the force needed to overcome gravity decreases.

How does friction affect an object on a ramp?

Friction is a force that opposes motion, and it can affect an object on a ramp in two ways. First, friction between the ramp and the object can cause the object to slow down or stop. Second, friction between the object and the ramp can cause the object to move down the ramp at a slower rate than expected.

How does the length of the ramp affect the motion of an object?

The length of the ramp affects the motion of an object by changing the distance the object needs to travel to reach the end of the ramp. A longer ramp will require the object to move a greater distance, which means it will take longer to reach the end. This can also affect the speed of the object, as it will have more time to accelerate or decelerate.

Can the height of the ramp affect the motion of an object?

Yes, the height of the ramp can affect the motion of an object. A higher ramp will require more force to move an object up it, as there is a greater component of force needed to overcome gravity. This can also affect the speed of the object, as it will have more potential energy at the top of the ramp, which can be converted into kinetic energy as it moves down the ramp.

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