Q: Eratosthenes measured the size of the Earth by observing the difference in the angle of the Sun's rays at noon in two cities. If the distance between the cities is 800 km and the angle difference is $$7.2^{\circ}$$, what is the calculated circumference of the Earth?

$$800 \times \frac{360}{7.2} = 40,000\ \text{km}$$

Q: A runner accelerates from rest to $$10\ \text{m/s} in$$ $$10\ \text{s}. $$What is their acceleration?

$$a = \frac{\Delta v}{\Delta t} = \frac{10\ \text{m/s}}{10\ \text{s}} = 1\ \text{m/s}^2$$

Q: A car travels $$150\ \text{km} in$$ $$3\ \text{hours}. $$What is its average speed?

$$\frac{150\ \text{km}}{3\ \text{h}} = 50\ \text{km/h}$$

Q: A $$2\ \text{kg}$$ object is acted upon by a net force of $$10\ \text{N}. $$What is its acceleration?

$$a = \frac{F}{m} = \frac{10\ \text{N}}{2\ \text{kg}} = 5\ \text{m/s}^2$$

Q: A $$5\ \text{kg}$$ object falls freely near the surface of the Earth. What is the force of gravity acting on it?

$$F = m \times g = 5\ \text{kg} \times 9.8\ \text{m/s}^2 = 49\ \text{N}$$

Q: A $$10\ \text{kg}$$ box is lifted $$2\ \text{m}$$ vertically. What is its gravitational potential energy relative to the ground?

$$PE = mgh = 10\ \text{kg} \times 9.8\ \text{m/s}^2 \times 2\ \text{m} = 196\ \text{J}$$

Question 1

Eratosthenes measured the size of the Earth by observing the difference in the angle of the Sun's rays at noon in two cities. If the distance between the cities is 800 km and the angle difference is $$7.2^{\circ}$$, what is the calculated circumference of the Earth?

Accepted Answer

$$800 	imes \frac{360}{7.2} = 40,000\ 	ext{km}$$

Question 2

Which of the following best describes a scientific hypothesis?

Accepted Answer

A statement that can be tested and potentially falsified by experiment or observation.

Question 3

A runner accelerates from rest to $$10\ 	ext{m/s} in$$ $$10\ 	ext{s}. $$What is their acceleration?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t} = \frac{10\ 	ext{m/s}}{10\ 	ext{s}} = 1\ 	ext{m/s}^2$$

Question 4

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 5

An object is in dynamic equilibrium. What is the net force acting on it?

Accepted Answer

$$0\ 	ext{N}$$

Question 6

A car travels $$150\ 	ext{km} in$$ $$3\ 	ext{hours}. $$What is its average speed?

Accepted Answer

$$\frac{150\ 	ext{km}}{3\ 	ext{h}} = 50\ 	ext{km/h}$$

Question 7

If the net force on an object is zero, which of the following statements is always true?

Accepted Answer

The object is in mechanical equilibrium.

Question 8

A $$2\ 	ext{kg}$$ object is acted upon by a net force of $$10\ 	ext{N}. $$What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{10\ 	ext{N}}{2\ 	ext{kg}} = 5\ 	ext{m/s}^2$$

Question 9

Which of the following best explains why you stay with the motion of the Earth when you jump in the air?

Accepted Answer

Because of inertia, your body retains the Earth's horizontal velocity.

Question 10

A $$5\ 	ext{kg}$$ object falls freely near the surface of the Earth. What is the force of gravity acting on it?

Accepted Answer

$$F = m 	imes g = 5\ 	ext{kg} 	imes 9.8\ 	ext{m/s}^2 = 49\ 	ext{N}$$

Question 11

If the speed of an object is doubled, what happens to its kinetic energy?

Accepted Answer

It increases by a factor of four.

Question 12

A $$10\ 	ext{kg}$$ box is lifted $$2\ 	ext{m}$$ vertically. What is its gravitational potential energy relative to the ground?

Accepted Answer

$$PE = mgh = 10\ 	ext{kg} 	imes 9.8\ 	ext{m/s}^2 	imes 2\ 	ext{m} = 196\ 	ext{J}$$

Question 13

Which of the following statements about machines is correct?

Accepted Answer

A machine can multiply force at the expense of distance.

Question 14

A lever is used to lift a $$100\ 	ext{kg}$$ load with an input force of $$500\ 	ext{N}. If $$the load is raised $$0.2\ 	ext{m}$$ and the input force moves $$1\ 	ext{m}$$, what is the efficiency of the lever?

Accepted Answer

$$	ext{Efficiency} = \frac{	ext{Output Work}}{	ext{Input Work}} 	imes 100\% = \frac{100\ 	ext{kg} 	imes 9.8\ 	ext{m/s}^2 	imes 0.2\ 	ext{m}}{500\ 	ext{N} 	imes 1\ 	ext{m}} 	imes 100\% = \frac{196}{500} 	imes 100\% = 39.2\%$$

Question 15

According to Newton's law of universal gravitation, what happens to the force between two masses if the distance between them is doubled?

Accepted Answer

The force becomes one-fourth as strong.

Question 16

A $$70\ 	ext{kg}$$ person stands on a scale in an elevator accelerating upward at $$2\ 	ext{m/s}^2. $$What is the scale reading?

Accepted Answer

$$F = m(g + a) = 70\ 	ext{kg} 	imes (9.8 + 2)\ 	ext{m/s}^2 = 70 	imes 11.8 = 826\ 	ext{N}$$

Question 17

Which of the following best describes the law of conservation of energy?

Accepted Answer

Energy cannot be created or destroyed, only transformed from one form to another.

Question 18

The gravitational force between two $$1\ 	ext{kg}$$ masses separated by $$1\ 	ext{m} is $$given by $$F = G \frac{m_1$ m_2$}{r^2$}. $$What is the value of $$F$$ using $$G = 6.67 	imes 10$$^{-11}$$\ 	ext{N}\cdot	ext{m}^2/	ext{kg}^2$$?

Accepted Answer

$$F = 6.67 	imes 10$$^{-11}$$\ 	ext{N}$$

Question 19

Which of the following is an example of recycled energy?

Accepted Answer

Heat from industrial processes used to generate electricity.

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