A ball weighing m = 300 g rolls down and rolls down an inclined chute with a length of l = 1.6 from the top

A ball weighing m = 300 g rolls down and rolls down an inclined chute with a length of l = 1.6 from the top point of the chute. When flat, the force of gravity performed the work A = 2.4 J. Determine the angle of inclination of the gutter to the horizon.

m = 300 g = 0.3 kg.

g = 10 m / s2.

l = 1.6 m.

A = 2.4 J.

∠α -?

The work of force A is determined by the formula: A = F * S * cosα, where F is the force that acts on the body, S is the displacement of the body under the action of the force, ∠α is the angle between the direction of action of the force F and displacement S.

The force of gravity F is always directed vertically downward and is determined by the formula: F = m * g, where m is the mass of the body, g is the acceleration of the body.

The movement of the ball S will be the length of the groove l: S = l.

The angle between gravity m * g and the gutter l will be the angle of inclination of the plane to the horizon.

A = m * g * l * cosα.

cosα = A / m * g * l.

cosα = 2.4 J / 0.3 kg * 10 m / s2 * 1.6 m = 0.5.

∠α = 60 °.

Answer: the gutter is at an angle ∠α = 60 ° to the horizon.