A block of ice with mass 2.00 kg slides 0.750 m down an inclined plane that slopes downward at a

step 1 In the given problem here this is the inclined slope which is inclined an angle of 36 .9 degree

A block of ice with mass 2.00 kg slides 0.750 m down an...

A block of ice with mass 2.00 $\mathrm{kg}$ slides 0.750 $\mathrm{m}$ down an inclined plane that slopes downward at an angle of $36.9^{\circ}$ below the horizontal. If the block of ice starts from rest, what is its final speed? You can ignore friction.

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Key Concepts

Conservation of Energy

This principle states that in a closed system, energy is neither created nor destroyed but only converted from one form to another. In problems like this where friction is ignored, the gravitational potential energy lost by the object as it descends is entirely transformed into kinetic energy, allowing for the determination of its final speed.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position within a gravitational field, typically given by the formula U = mgh. In inclined plane problems, the vertical height h is related to the slant distance of the incline and the sine of the angle, which is a crucial step in calculating the energy change.

Kinetic Energy

Kinetic energy is the energy an object possesses because of its motion, expressed by the formula KE = ½mv². In a frictionless scenario, the increase in kinetic energy as an object moves down an incline comes from the decrease in gravitational potential energy.

Trigonometry in Inclined Plane Problems

Trigonometric relationships are used to relate the geometry of the inclined plane to physical quantities. Specifically, the sine of the incline angle is used to calculate the vertical displacement from the slant distance, which is essential for computing the change in gravitational potential energy.

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