Block on Inclined Plane: Velocity & Displacement Eqns & Calcs

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In summary, a 64-lb block released from the top of a plane inclined at 30 degrees to the horizontal slides down with a coefficient of friction of 0.25 and experiences a drag force due to air resistance equal to one-half its velocity in ft/sec. To determine the equation for the velocity and displacement of the block, write F=ma and substitute the expressions for each force and acceleration. This will give you the differential equation to solve.
  • #1
frenika
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Problem: A 64-lb block is released from the top of a plane inclined at 30 degrees to the horizontal. As the block slides down the plane, its coefficient of friction is 0.25, and it experiences a drag force due to air resistance equal to one-half is velocity in ft/sec. (a) Determine the equation for the velocity of the block. (b) Determine the equation for the displacement of the block, (c) Calculate the displacement and velocity of the block 5 sec after it is released.
 
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  • #3
I understand the formulas for the force and everything but I need help setting up the differential equation
 
  • #4
After you have expressions for each of the forces and for the acceleration, write
[tex]F = ma[/tex]
Then, beneath that, in the corresponding positions, rewrite it using the expressions you found. That will give you the differential equation you have to solve.
 

What is the block on an inclined plane?

The block on an inclined plane is a physics problem that involves a block of mass moving on an inclined surface. It is a commonly used example in physics to illustrate the concepts of force, gravity, and motion.

What are the equations used to calculate the velocity and displacement of the block on an inclined plane?

The equations used to calculate the velocity and displacement of the block on an inclined plane are the same as those used for any object in motion with constant acceleration. These equations are v = u + at (velocity equation) and s = ut + 1/2at^2 (displacement equation), where v is the final velocity, u is the initial velocity, a is the acceleration, t is the time, and s is the displacement.

How do I determine the angle of the inclined plane in the block on an inclined plane problem?

The angle of the inclined plane can be determined by using trigonometric functions such as sine, cosine, and tangent. The angle can be calculated by taking the inverse sine, cosine, or tangent of the ratio of the height of the inclined plane to its length.

What are the units of measurement for velocity and displacement in the block on an inclined plane problem?

The units of measurement for velocity are meters per second (m/s) and for displacement are meters (m). However, the units can vary depending on the units used for mass, time, and acceleration in the equations.

Can the equations for velocity and displacement be used for any object on an inclined plane?

Yes, the equations for velocity and displacement can be used for any object on an inclined plane, as long as the object has constant acceleration. These equations are based on the principles of motion and can be applied to any object in motion, including the block on an inclined plane.

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