Question

modified true/false circle true or false first. if false, change the incorrect word or phrase. 2 marks - k/u

1. if the force and displacement are perpendicular to each other, there is no work done.

true / false

1. mechanical energy is calculated by subtracting kinetic energy from gravitational potential energy.

true / false
multiple choice circle the choice that best completes the statement or answers the question. 10 marks - k/u

1. a 7.0 kg object is moving forward with an applied force of 20.0 n right, displacing 6.0 m. the total work done due to the force of gravity on the object is:

a. 140 j b. 840 j c. 42 j d. 120 j e. 0 j

1. the kinetic energy of a 12 kg object moving at a speed of 8.0 m/s would be:

a. 380 j b. 96 j c. 770 j d. 940 j e. 0 j

1. which of the following is equivalent to the units of a joule (j)?

a. n/m b. n·kg c. kg·\\(\frac{m}{s^{2}}\\) d. kg·\\(\frac{m^{2}}{s^{2}}\\) e. \\(m/s^{2}\\)

1. a 45.0 kg object with 3550 j of gravitational potential energy would be at a height of:

a. 78.9 m b. 362 m c. 2.84 m d. 0 m e. 8.05 m

1. what is the power required to lift a 7.5 kg object to a height of 11 m in 5.0 s?

a. 810 w b. 160 w c. 410 w d. 4.0 × 10³ w e. over 9000!

1. an object is accelerated by a force from rest to 20.0 m/s in 5.0 seconds. if the process is repeated for another trial, but only takes 2.5 s, which statement below is true?

a. the second trial requires less power.
b. both trials require the same power.
c. the work done in both trials is equal.
d. the work done in the first trial is more.
e. none of the statements are true.

1. a downhill skier is at rest at a height of 65.0 m. if the process is only 38% efficient, what will be the skiers speed at the bottom of the hill?

a. 220 m/s b. 29 m/s c. 2.9 m/s d. 22 m/s e. 25 m/s

1. which of the following energy sources is considered non - renewable?

a. fossil fuels (oil, natural gas, coal etc.)
b. nuclear power
c. wind
d. solar power
e. both (a) and (b)

1. using the diagram to the right, at which point will the object have the highest amount of kinetic energy?

a. a b. b c. c d. d e. the kinetic energy is equal everywhere.

1. using the same diagram, at which point will the object have the highest amount of mechanical energy?

a. a b. b c. c d. d e. the mechanical energy is the same everywhere.

Explanation:

Step1: Analyze question 1

The work formula is \(W = Fd\cos\theta\). When \(\theta = 90^{\circ}\), \(\cos\theta=0\), so \(W = 0\).

Step2: Analyze question 2

Mechanical energy \(E = E_{k}+E_{p}\) (kinetic energy + gravitational potential energy), not \(E = E_{p}-E_{k}\).

Step3: Analyze question 3

The force of gravity \(F = mg\) acts vertically. The displacement is horizontal. \(\theta = 90^{\circ}\), using \(W = Fd\cos\theta\), \(W = 0\).

Step4: Analyze question 4

Kinetic energy formula \(E_{k}=\frac{1}{2}mv^{2}\). Substitute \(m = 12\space kg\), \(v = 8.0\space m/s\), \(E_{k}=\frac{1}{2}\times12\times8^{2}=384\approx380\space J\).

Step5: Analyze question 5

From \(W = Fd\), \(F = ma\) (Newton's second law \(F = ma\), \(a=\frac{m}{s^{2}}\)), \(W=(kg\cdot\frac{m}{s^{2}})\cdot m=kg\cdot\frac{m^{2}}{s^{2}}\).

Step6: Analyze question 6

Gravitational potential energy formula \(E_{p}=mgh\). Solve for \(h\): \(h=\frac{E_{p}}{mg}\). Substitute \(m = 45.0\space kg\), \(E_{p}=3550\space J\), \(g = 9.8\space m/s^{2}\), \(h=\frac{3550}{45\times9.8}\approx8.05\space m\).

Step7: Analyze question 7

Power formula \(P=\frac{W}{t}\), \(W = mgh\). Substitute \(m = 7.5\space kg\), \(h = 11\space m\), \(t = 5.0\space s\), \(g = 9.8\space m/s^{2}\), \(P=\frac{7.5\times9.8\times11}{5}=161.7\approx160\space W\).

Step8: Analyze question 8

Work \(W=\Delta E_{k}=\frac{1}{2}m(v^{2}-u^{2})\). Since \(u = 0\) and \(v\) is the same, \(W\) is the same. Power \(P=\frac{W}{t}\). Smaller \(t\) means larger \(P\).

Step9: Analyze question 9

Initial gravitational potential energy \(E_{p}=mgh\). Final kinetic energy \(E_{k}=\frac{1}{2}mv^{2}\). With efficiency \(\eta = 0.38\), \(0.38mgh=\frac{1}{2}mv^{2}\). Solve for \(v\): \(v=\sqrt{2\times0.38\times g\times h}\). Substitute \(h = 65.0\space m\), \(g = 9.8\space m/s^{2}\), \(v=\sqrt{2\times0.38\times9.8\times65}\approx22\space m/s\).

Step10: Analyze question 10

Fossil fuels (a) are non - renewable. Nuclear power (b) uses uranium which is non - renewable (in the context of current technology and fuel sources). Wind (c) and solar (d) are renewable.

Step11: Analyze question 11

Kinetic energy is highest at the lowest point (point C) as potential energy is converted to kinetic energy.

Step12: Analyze question 12

In the absence of non - conservative forces (assuming ideal conditions in the diagram), mechanical energy \(E = E_{k}+E_{p}\) is conserved.

Answer:

1. True
2. False, change “subtracting kinetic energy from gravitational potential energy” to “adding kinetic energy and gravitational potential energy”
3. e. \(0J\)
4. a. \(380J\)
5. d. \(kg\cdot\frac{m^{2}}{s^{2}}\)
6. e. \(8.05m\)
7. b. \(160W\)
8. c. The work done in both trials is equal.
9. d. \(22m/s\)
10. e. Both (a) and (b)
11. c. C
12. e. The mechanical energy is the same everywhere.