# Determining tension

• May 25th 2010, 10:46 AM
Neconine
Determining tension
An 18-kg is held in equilibrium on the surface of a frictionless ramp inclined at 25 degrees to the horizontal. A rope is attached to the crate at an angle of 15 degrees to the surface of the ramp. Determine the tension in the rope that is required to hold the crate in equilibrium.
• May 25th 2010, 11:33 AM
AllanCuz
Quote:

Originally Posted by Neconine
An 18-kg is held in equilibrium on the surface of a frictionless ramp inclined at 25 degrees to the horizontal. A rope is attached to the crate at an angle of 15 degrees to the surface of the ramp. Determine the tension in the rope that is required to hold the crate in equilibrium.

We need to decompose our forces.

Since there is no friction, we need the gravity component of the 18kg mass in the direction of the surface to equal the tension component of the rope in the direction along the surface.

This means,

$(18*9.8) sin(25) = Tcos15$

Solve for T.

The 18*9.8 represents the force in Newtons of the mass on the surface. The sin/cos come from the construction of triangles and equating the Tension with the Force of the Weight in the same direction (along the surface of the ramp)