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TFrc23 Simple Incline Plane

A simple 45^o incline plane has 25 kg hanging and 45 kg along the incline.

Find the acceleration and the tension in the cord?

Draw a diagram of the system.

frc23drw01.gif (2662 bytes)

Guessing at the direction of the acceleration again is not so simple in this problem. Don't agonize over it. Choose counterclockwise and proceed with the vector diagram. The 25 kg mass presents no problem. For the 45 kg mass we need the component of the gravitational force down the plane.

Draw the vector diagram.

frc23drw02.gif (3455 bytes)

Write the force equations for each of the masses.

frc23drw03.gif (1505 bytes)

Again T₁= T₂ so add

frc23drw04.gif (1361 bytes)

and