A marble rolls down a slope at a velocity of 10 m/s. If the kinetic energy of the marble is 2 J, what is the mass of the marble?

Question

A marble rolls down a slope at a velocity of 10 m/s.  If the kinetic energy of the marble is 2 J, what is the mass of the marble?

Quizplus · Accepted Answer

11ecba2d_1323_a3ce_a3bf_85b629fac99b_MD0008_00 Gravitational potential energy and kinetic energy are two forms of energy that an object may possess in mechanical systems. Gravitational potential energy is energy that is stored based on an object's position relative to a reference point within a gravitational field. Consequently, potential energy is often referred to as the "energy of position." Kinetic energy is the energy possessed by an object in motion, whether that object is rotating or moving through space via translational motion. Consequently, kinetic energy may be referred to as the "energy of motion," and the magnitude of the kinetic energy (KE) is determined by the mass (m) and velocity (v) of a moving object: 11ecba2d_1323_a3cf_a3bf_95807c306edf_MD0008_00 The SI unit for energy is the joule (J), where 1 joule is equal to the product of mass (kg) and velocity (m/s) squared (1 J = 1 kg·m²·s⁻²). Certain mechanical processes may convert energy from one form to another. For example, an object falling from a height loses gravitational potential energy and gains kinetic energy. However, the total energy of an object is always conserved. In this question, a marble has 2 J of kinetic energy as it rolls down a slope at a velocity of 10 m/s. Provided that no forces other than gravity act on the marble to cause motion, it can be assumed that all of this kinetic energy was attained through the conversion of its gravitational potential energy. The mass of the marble can be determined by substituting given values and solving for mass in the equation for the kinetic energy of an object: 11ecba2d_1323_cae0_a3bf_1bf1d73edc2f_MD0008_00 11ecba2d_1323_cae1_a3bf_57052f04cef7_MD0008_00 11ecba2d_1323_cae2_a3bf_73754793e31e_MD0008_00 Therefore, the marble has a mass of 0.04 kg, or 40 g (Choice B). Educational objective: Kinetic energy (often expressed in SI units using the joule) is a form of mechanical energy that has a magnitude directly proportional to the mass and the square of the velocity of an object.

A Marble Rolls Down a Slope at a Velocity of 10