U is correct on the first one
Dependent variable is your answer.
<span>When temperature increases, particles in an object speed up, which means an increase in thermal energy. Since the particles are moving more now, the potential energy decreases, therefore kinetic energy increases.
Overall, when temp goes up, thermal energy goes up, which leads to an increase in kinetic energy.</span>
<span>14.79 m/s
At the top of the loop, there's 2 opposing forces. The centripetal force that's attempting to push the roller coaster away and the gravitational attraction. These 2 forces are in opposite directions and their sum is 0.80 mg where m = mass and g = gravitational attraction. So let's calculate the amount of centripetal force we need.
0.80 = F - 1.00
1.80 = F
So we need to have a centripetal force that's 1.8 times the local gravitational attraction which is 9.8 m/s^2. So
1.8 * 9.8 m/s^2 = 17.64 m/s^2
The formula for centripetal force is
F = mv^2/r
where
F = force
m = mass
v = velocity
r = radius
We can eliminate mass from the equation since the same mass is being affected by both the centripetal force and gravity. So:
F = v^2/r
17.64 m/s^2 = v^2/12.4 m
218.736 m^2/s^2 = v^2
14.78972616 m/s = v
So the velocity at the top of the loop (rounded to 2 decimal places) is 14.79 m/s.</span>
