Equations of Motion: Solving the Problem and Finding Velocity Limits

In summary, the problem involves determining the equation of motion for a point particle under the influence of both gravitational and friction forces. It is shown that when the particle starts at rest, its velocity cannot exceed mg/k. The calculations have been attached, but there seems to be an issue when the incline is almost flat. However, this is not possible as the problem does not mention an incline or a normal force. The solution involves solving the equation of motion for F=Fgrav-kv and showing that v(t) is a monotonous function that approaches mg/k as t approaches infinity.
  • #1
Logarythmic
281
0
The problem is to determine the equation of motion for a point particle on which both the gravitational force and a friction force of magnitude
[tex]|\vec{F}_fr| = k|\vec{v}|[/tex]
act and to show that when the particle starts at rest, its velocity cannot exceed mg/k.
I have attached my calculations but something is wrong. The velocity cannot increase when the incline is almost flat..?
 
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  • #2
Incline? You can't be on an incline since additionally, there is a normal force. The problem makes no mention of such thing.

Just solve the equation of motion for F=Fgrav-kv. Plug in the initial value v0=0 and show that v(t) is a monotonous function that converge assymptotically towards mg/k as t-->+infty.
 
  • #3
Of course. Thanks :)
 

FAQ: Equations of Motion: Solving the Problem and Finding Velocity Limits

What are the equations of motion?

The equations of motion are mathematical formulas that describe the relationship between an object's position, velocity, acceleration, and time. These equations are used to solve problems involving the motion of objects.

How do you solve problems using equations of motion?

To solve problems using equations of motion, you first need to identify the given variables such as initial and final positions, velocities, accelerations, and time. Then, you can use the appropriate equation(s) to solve for the unknown variable. It is important to pay attention to units and use consistent units throughout the problem.

What is the importance of finding velocity limits?

Finding velocity limits is important because it allows us to understand the maximum or minimum velocity that an object can reach during its motion. This information is crucial for designing safe and efficient systems, such as vehicles, roller coasters, and aircraft.

How do you find velocity limits using equations of motion?

To find velocity limits using equations of motion, you can set up the appropriate equation and solve for the maximum or minimum velocity. For example, to find the maximum speed of a falling object, you can use the equation v^2 = v0^2 + 2as, where v is the final velocity, v0 is the initial velocity, a is the acceleration due to gravity, and s is the displacement.

Can equations of motion be used for curved motion?

Yes, equations of motion can be used for curved motion. However, in this case, the equations will be a bit more complex as they will involve both linear and angular quantities such as linear and angular velocities and accelerations. For example, in circular motion, the equation v = rw can be used, where v is the linear velocity, r is the radius of the circle, and w is the angular velocity.

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