4.A student with a mass of m rides a roller coaster with a loop with a radius of curvature of r. What is the minimum speed the rollercoaster can maintain and still make it all the way around the loop

v = √gr

Explanation:

In order for the roller coaster to make it all the way around the loop, the centripetal force at the top of the rider must be equal to the weight the student. So, that the student does not fall during the motion. Therefore,

Centripetal Force = Weight

mv²/r = mg

v²/r = g

v² = gr

Taking square root on both sides, we get:

v =  √gr

where,

v = speed of roller coaster

r = radius of curvature

g = acceleration due to gravity

Hence, the minimum speed the roller coaster can maintain and still make it all the way around the loop, is found to be:

v = √gr

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.