The angle θ is slowly increased. write an expression for the angle at which the block begins to move in terms of μs.

Explanation:

An object is at rest along a slope if the net force acting on it is zero. The equation of the forces along the direction parallel to the slope is:

(1)

where

is the component of the weight parallel to the slope, with m being the mass of the object, g the acceleration of gravity, the angle of the slope

is the frictional force, with being the coefficient of friction and R the normal reaction of the incline

The equation of the forces along the direction perpendicular to the slope is

where

R is the normal reaction

is the component of the weight perpendicular to the slope

Solving for R,

And substituting into (1)

Re-arranging the equation,

This the condition at which the equilibrium holds: when the tangent of the angle becomes larger than the value of , the force of friction is no longer able to balance the component of the weight parallel to the slope, and so the object starts sliding down.

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2