Question

potential & kinetic energy
name:

1. where does the roller coaster have the most potential energy? a b c d e
2. where does the roller coaster have the least potential energy? a b c d e
3. where does the roller coaster have the most kinetic energy? a b c d e
4. where does the roller coaster have the least kinetic energy? a b c d e
5. where is potential energy decreasing? a b c d e
6. where is potential energy increasing? a b c d e
7. where is kinetic energy decreasing? a b c d e
8. where is kinetic energy increasing? a b c d e
9. which location which has more potential energy than b a b c d e
10. which location has more kinetic energy than e? a b c d e

Explanation:

Step1: Recall the formula for potential energy

Potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height). Higher the height \(h\), more the potential energy.

Step2: Recall the formula for kinetic energy

Kinetic energy \(K=\frac{1}{2}mv^{2}\) (where \(m\) is mass, \(v\) is velocity). Lower the height (due to conservation of mechanical energy \(E = U + K\), assuming no non - conservative forces), higher the velocity \(v\) and more the kinetic energy.

1. For the most potential energy:

Since \(U = mgh\), the highest point has the most potential energy. Point \(D\) is the highest.

1. For the least potential energy:

The lowest point has the least potential energy. Point \(C\) is the lowest.

1. For the most kinetic energy:

Since \(K=\frac{1}{2}mv^{2}\) and using conservation of energy (\(E=U + K\)), the lowest point (where \(U\) is least) has the most \(K\). Point \(C\)

1. For the least kinetic energy:

The highest point (where \(U\) is most) has the least \(K\). Point \(D\)

1. Potential energy decreasing:

When the roller - coaster is going down (decreasing \(h\)), \(U\) is decreasing. From \(D\) to \(E\) and from \(B\) to \(C\)

1. Potential energy increasing:

When the roller - coaster is going up (increasing \(h\)), \(U\) is increasing. From \(A\) to \(B\) and from \(C\) to \(D\)

1. Kinetic energy decreasing:

When \(U\) is increasing (going up, so \(v\) is decreasing as \(E = U+K\) is constant), \(K\) is decreasing. From \(A\) to \(B\) and from \(C\) to \(D\)

1. Kinetic energy increasing:

When \(U\) is decreasing (going down, so \(v\) is increasing as \(E = U + K\) is constant), \(K\) is increasing. From \(D\) to \(E\) and from \(B\) to \(C\)

1. More potential energy than \(B\):

Points with higher \(h\) than \(B\). Point \(D\)

1. More kinetic energy than \(E\):

Since \(K=\frac{1}{2}mv^{2}\) and \(E\) is at a higher position than \(C\) (using \(E = U+K\)), point \(C\)

Answer:

1. D
2. C
3. C
4. D
5. B - C and D - E
6. A - B and C - D
7. A - B and C - D
8. B - C and D - E
9. D
10. C