![]() Some amount of energy is lost when the clay deforms and sticks to the turntable! This change in energy is given by: To calculate ω₁ we use the following formula:Ĭalculate the loss of energy to thermal energyĮnergy is not conserved. = The moment of inertia of a cylinder with mass m and radius r around its z axis = ½mr²., and can be calculated as followed: With ω1 = the angular speed after (ω1 = ω0*) The angular momentum before must be equal to the angular momentum after. ![]() The angular momentum is defined as: L = I*ω The loss of energy to thermal energy is 965.6 JĬonservation of angular momentum says that 'the angular momentum must be the same before and after the clump of clay is attached to the turntable'. Read more about Momentum here /question/25121535 This value is negative which signifies 965.6 J being lost in the form of thermal energy. Ω₁ = I₀ω₀ / I₁ = 152.46*8.5/ 184.86 = 7.01 rad/sĮnergy is not conserved as some amount of energy is lost when the clay deforms and sticks to the turntable. The moment of inertia of a cylinder = ½mr² I₀ = The moment of inertia of the turntable Where I is the moment of inertia, w is the angular speedĪngular momentum after: La = (It + Ic)*ω1 This is defined as the property of any rotating object given by moment of inertia times angular velocity.Ĭonservation of angular momentum says that the angular momentum is constant except an external torque is applied. The loss of energy to thermal energy is 965.6 J.The angular speed of the clay is 7.01 rad/s.Learn more about direction of force for positive and negative charges here: /question/19076014 A positive charge moving downward in a magnetic field that points upward, the force will point downwards.A positive charge moving upward in an electric field that points out of the screen, the force will point out of the screen.A positive charge moving into the screen in a magnetic field that points upward, the force will point into the screen.A negative charge within an electric field that points upward, the direction of the force is downwards.A positive charge within an electric field that points to the left, the force will point to the left.(D) The force will point out of the screen.īy convention the electric field and force are always pointing the same way for a positive charge and opposite for a negative charge. (C) The force will point into the screen. (B) The direction of the force is downwards. Now, we need to know the distance travelled up the incline, which is related with the height h, by the angle that the incline does with the horizontal, as follows: Simplifying, and taking g = 9.8 m/s², we can find h: So, in this case, we can put the following:Ĭ) Now, if we assume that there is no friction between the bike and the ground, all the kinetic energy must become gravitational potential energy, at some height h. In this case, as the force is parallel to the displacement, work is directly equal to the product of the applied force times the displacement (in magnitude), so we can write the following:ī) In absence of friction, the work done by the force is equal to the change in the kinetic energy, as it can be showed using the work-energy theorem. Learn more: /question/24509770Ī) By definition, work, is the process that does an applied force, in order to produce a displacement in the same direction than the applied force, and can be written as follows Given the hill has an angle of 8.29 ° with the horizontal, we can calculate the distance (d) traveled using the following trigonometric equation. If the cyclist starts coasting at the bottom of the hill, the potential energy (P) at the maximum point will be equal to the kinetic energy at the bottom. Since it starts from rest, the initial kinetic energy is zero. We can calculate the work (w) done by the bicyclist using the following expression.īefore the hill, we can state that the work done is equal to the change in the kinetic energy (K), according to the work-energy theorem. If the cyclist starts coasting at the bottom of the hill, it travels 320 m.Ī bicyclist starts from rest applies a force of 195 N (F) to ride his bicycle across a flat ground for a distance of 290 m (d). A bicyclist must do a work of 5.66 × 10⁴ J to apply a force on the bicycle of 195 N for 290 m and achieve a speed of 30.1 m/s.
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