Determining how far a body will move up an inclined plane and the time to reach the highest point

In summary, determining how far a body moves up an inclined plane involves analyzing the initial velocity, angle of inclination, and gravitational force acting on the body. The distance traveled can be calculated using kinematic equations, factoring in the acceleration due to gravity and the incline's angle. Additionally, the time to reach the highest point is derived from these equations, taking into account the initial speed and the deceleration caused by gravity along the slope. Understanding these principles allows for accurate predictions of motion along an inclined plane.
  • #1
tremain74
12
3
Homework Statement
A body is projected up a 25 degree plane with an initial velocity of 15 m/s. If the coefficient of friction between the body and the plane is 0.25, determine how far the body will move up the plane and the time required to reach the highest point. Answer : 17.7 m, 2.36 s.
Relevant Equations
I tried to use the equation summation of force = p - 0.25N = ma.
15cos25 - 0.25N = ma.
 
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  • #2
Can you please show all of your work and explain why you are using that approach?
 
  • #3
berkeman said:
Can you please show all of your work and explain why you are using that approach?
I have tried to used the drawing pad last night to show my work but I am having trouble using it.
 
  • #4
Maybe start by talking us through your method...
 
  • #5
I have an object that is going up the plane at 25 degrees to the right. It is going at 15 m/s. I drew a free body diagram of the object. I have a P force at 15 m/ s going up the direction at 25 degrees. I also have friction force going in the opposite direction of 0.25 * N.
 
  • #6
tremain74 said:
I have a P force at 15 m/ s going up the direction at 25 degrees.
There is no force up the inclined plane. That 15m/s is the initial velocity up the plane.

You have probably worked through problems where was no frictional force for inclined planes, right? In those cases, you can just use Energy considerations to do the calculation for how far the object makes it up the inclined plane, right? How would you do this is there no friction?

And then, what changes (or additional terms) would you need to include in order to accommodate the frictional force? Does the frictional force back down the inclined plane change with the object's velocity?
 

FAQ: Determining how far a body will move up an inclined plane and the time to reach the highest point

1. What factors affect how far a body will move up an inclined plane?

The distance a body moves up an inclined plane is influenced by several factors, including the initial velocity of the body, the angle of the incline, the coefficient of friction between the body and the surface of the incline, and the mass of the body. The gravitational force acting on the body also plays a crucial role in determining how far it will ascend before coming to a stop.

2. How can I calculate the maximum height reached by a body on an inclined plane?

To calculate the maximum height reached by a body on an inclined plane, you can use the conservation of energy principle. The initial kinetic energy of the body is converted into gravitational potential energy at the highest point. The formula is: \[ \frac{1}{2}mv^2 = mgh \]where \( m \) is the mass, \( v \) is the initial velocity, \( g \) is the acceleration due to gravity, and \( h \) is the height. By rearranging the equation, you can solve for \( h \).

3. How do I determine the time it takes to reach the highest point on the incline?

The time to reach the highest point can be determined using kinematic equations. If you know the initial velocity and the acceleration (which is affected by gravity and the incline angle), you can use the equation:\[ v_f = v_i + at \]where \( v_f \) is the final velocity (0 at the highest point), \( v_i \) is the initial velocity, \( a \) is the acceleration (negative due to gravity), and \( t \) is the time. Rearranging gives:\[ t = \frac{v_f - v_i}{a} \]You can solve for \( t \) once you have the values for \( v_i \) and \( a \).

4. How does friction impact the distance traveled up the incline?

Friction opposes the motion of the body moving up the incline, which reduces the distance it can travel. The frictional force can be calculated using the formula:\[ F_f = \mu N \]where \( \mu \) is the coefficient of friction and \( N \) is the normal force. The presence of friction means that some of the initial kinetic energy is converted into heat rather than being used to move the body up the incline, resulting in a shorter distance traveled compared to a frictionless scenario.

5. Can I apply these principles to different angles of incline?

Yes, the principles of motion on an inclined plane can be applied to different angles of incline. However, the angle affects the component of gravitational force acting along the plane, which in turn

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