Final answer:
To calculate the speed and normal reaction force of an ice cube sliding around a loop-the-loop, principles of conservation of energy and circular motion dynamics are applied, considering height and radius given.
Step-by-step explanation:
To solve the physics problem involving an ice cube sliding around a loop-the-loop track, we will apply the principles of conservation of energy and circular motion dynamics. Given the height h = 3.5 r, where r = 0.5 m, we first calculate the speed of the ice cube at point B, located at the top of the loop.
Using the conservation of mechanical energy, where potential energy at the top converts to kinetic energy at the bottom, we can find the speed at B using the equation: 1/2 * m * v2 = m * g * h. With g being the acceleration due to gravity (9.81 m/s2), and plugging the values for h, we can solve for v.
To find the normal reaction force at point B, we use the circular motion equation: Normal force = m * v2/r - m * g, considering that at the top of the loop, the normal force is the difference between the centripetal force and weight.
For the normal force at point C, which is at the bottom of the loop, we use a similar circular motion equation: Normal force = m * v2/r + m * g, as the normal force here is the sum of the centripetal force and weight due to the direction of the force of gravity.
The speed at point C is the same as that at point B if we consider energy conservation and disregard any energy losses along the track.