A solid sphere of mass 2 kg is rolling
without slipping on a table with linear
speed of 0.5 m/s. Calculate its total kinetic
energy.
To calculate the total kinetic energy of the rolling solid sphere, we need to consider two types of kinetic energy: translational kinetic energy and rotational kinetic energy.
Translational kinetic energy (KE_trans) is the energy associated with the linear motion of the object. It can be calculated using the formula:
KE_trans = (1/2) * mass * velocity^2
In this case, the mass of the sphere (m) is given as 2 kg and the linear speed (v) is given as 0.5 m/s. Plugging these values into the formula, we get:
KE_trans = (1/2) * 2 kg * (0.5 m/s)^2
= 0.5 J
Rotational kinetic energy (KE_rot) is the energy associated with the rotation of the object. For a solid sphere rolling without slipping, its rotational kinetic energy is related to its moment of inertia (I) and angular velocity (ω) by the formula:
KE_rot = (1/2) * I * ω^2
The moment of inertia of a solid sphere rotating about its central axis is given by:
I = (2/5) * m * r^2
where m is the mass of the sphere and r is its radius. In this case, the mass of the sphere (m) is given as 2 kg. The radius (r) is not provided, so we cannot directly calculate the rotational kinetic energy.
Therefore, to determine the total kinetic energy, we need to know either the radius of the sphere or the angular velocity. With the given information, we can only calculate the translational kinetic energy, which is 0.5 J.
well, the equation for kinetic energy is this:
KE = (1/2)mv^2
therefore...
KE = (1/2)(2 kg)(0.5 m/s)^2
KE = 0.25 J
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