Gravity and Inclined Planes

Incline Planes

Steps to solving inclined plane

• draw free body diagram

• Identify the individual forces

• use trig functions to account for angle of incline for each force

• solve

Forces

• FN=perpendicular (y) =mg cos ( $\theta$  )

• Fll= parallel (x) = net if no other force is acting on i

• Ff= is the frictional force opposite to Fll or Fa =  $\mu$  mg cos ( $\theta$  )

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a 43 kg box is on a frictionless 32 degree inclined plane. What is the F_g

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a 43 kg box is on a frictionless 32 degree inclined plane. What is the F_N

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a 43 kg box is on a frictionless 32 degree inclined plane. What is the F_ll

Solving with friction

• F_net is the sum of all forces

• F_net= F_ll+ F_f +F_a

• remember that forces can act in opposite directions

Friction

= $\mu$  mg cos  $\theta$  

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a 43 kg box is on a 32 degree inclined plane with a friction coefficient of .23 What is the F_net

F_a = applied force

an applied force can be either a push or a pulling force and is usually opposite of the parallel force

*NOTE*

when drawing your free body/solving for net force keep in mind that frictional force is dependent on the direction of the objects movement

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a 43 kg box is on a 32 degree inclined plane with a friction coefficient of .23. A rope holds the box preventing it from sliding down the ramp. what is the tension on the rope?

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A 20 kg box is pulled up an incline of 60 degrees on a surface that has a frictional coefficient of .09. With an applied force of 221 N. What is the resulting force