Q: Assuming the Bohr model of the atom, an electron in Li$$^{2+}$$ emits a photon of wavelength $$13.5\ \mathrm{nm}$$ for the transition $$n = 2 to$$ $$n = 1. If $$you treat the atom like an electron in a one-dimensional box, what is the width of the box that would allow the emission of a photon of this wavelength? What is the ground state energy of a box with this width? Is a one-dimensional box a suitable model for the Bohr atomic model?

i) $$1.92 \times 10$$^{-10}$$\ \mathrm{m} ii$$) $$90.9\ \mathrm{eV}$$ iii) Not a suitable model

Q: A photon of light bounces back into its initial direction of motion after colliding with an electron. The angle between the initial and final direction of the photon is $$180^\circ. $$The wavelength of the photon increases by $$5\%$$ following the scattering. Determine the wavelength of the incident photon.

$$4.62 \times 10$$^{-12}$$\ \mathrm{m}$$

Q: If a ceramic coffee mug, with a height of $$10.0\ \mathrm{cm}$$ and a diameter of $$8.00\ \mathrm{cm}$$, had the same density as a neutron or a proton, what would be its approximate mass?

$$3.99 \times 10$$^{17}$$\ \mathrm{kg}$$

Q: A cylinder with a $$6.3\ \mathrm{cm}$$ diameter is $$14.4\ \mathrm{cm} in $$length. In standard international (SI) units, how much volume does the cylinder occupy?

$$449 \times 10$$^{-6}$$\ \mathrm{m}^3$$

Question 1

Assuming the Bohr model of the atom, an electron in Li$$^{2+}$$ emits a photon of wavelength $$13.5\ \mathrm{nm}$$ for the transition $$n = 2 to$$ $$n = 1. If $$you treat the atom like an electron in a one-dimensional box, what is the width of the box that would allow the emission of a photon of this wavelength? What is the ground state energy of a box with this width? Is a one-dimensional box a suitable model for the Bohr atomic model?

Accepted Answer

i) $$1.92 	imes 10$$^{-10}$$\ \mathrm{m} ii$$) $$90.9\ \mathrm{eV}$$ iii) Not a suitable model

Question 2

A photon of light bounces back into its initial direction of motion after colliding with an electron. The angle between the initial and final direction of the photon is $$180^\circ. $$The wavelength of the photon increases by $$5\%$$ following the scattering. Determine the wavelength of the incident photon.

Accepted Answer

$$4.62 	imes 10$$^{-12}$$\ \mathrm{m}$$

Question 3

In an experiment, $$7.2\ \mathrm{g} of $$potassium chloride is added for every liter of water. Using the conversion factor $$1\ \mathrm{mL} = 1\ \mathrm{cm}^3$$, write the salt concentration in terms of $$\mathrm{kg}/\mathrm{m}^3.$$

Accepted Answer

$$2.7\ \mathrm{kg}/\mathrm{m}^3$$

Question 4

If a ceramic coffee mug, with a height of $$10.0\ \mathrm{cm}$$ and a diameter of $$8.00\ \mathrm{cm}$$, had the same density as a neutron or a proton, what would be its approximate mass?

Accepted Answer

$$3.99 	imes 10$$^{17}$$\ \mathrm{kg}$$

Question 5

A car is moving with speed $$v$$, given by the equation $$v = C + Dt^2$, where t$ represents time and C$ and D$ are constants. Determine the SI units of C$ and D$.

Accepted Answer

C $$(\mathrm{m}/\mathrm{s})$$, D $$(\mathrm{m}/\mathrm{s}^3)$$

Question 6

Find the number of significant figures in $$3.254 	imes 10^4$.

Accepted Answer

four

Question 7

A cylinder with a $$6.3\ \mathrm{cm}$$ diameter is $$14.4\ \mathrm{cm} in $$length. In standard international (SI) units, how much volume does the cylinder occupy?

Accepted Answer

$$449 	imes 10$$^{-6}$$\ \mathrm{m}^3$$

Question 8

Refer to the motion diagram and position-time graphs. Which position-time graph best represents the motion of the RC car shown in the motion diagram and burst mode photo sequence?

Accepted Answer

The third image (position increases linearly with time, evenly spaced points)

Question 9

A lubricating oil is driven through a pipe using an electric pump. The speed of an oil particle is plotted in the first $$10\ \mathrm{s} of $$operation as shown in the velocity-time graph. Determine the acceleration of an oil particle through every stage shown on the graph.

Accepted Answer

First stage $$a = 3.5\ \mathrm{m}/\mathrm{s}^2$$; Second stage $$a = -0.6\ \mathrm{m}/\mathrm{s}^2$$; Third stage $$a = 0\ \mathrm{m}/\mathrm{s}^2$$

Question 10

A boat comes to a stop due to a malfunctioning engine. The velocity vs time graph of the boat is shown. Determine the approximate distance the boat moves in meters before it stops.

Accepted Answer

$$65\ \mathrm{m}$$

Question 11

The velocity-time graph for a body starting from rest is shown. Determine if there is any turning point for this moving body.

Accepted Answer

There is no turning point in this graph.

Question 12

A car is initially moving at a velocity of $$5.0\ \mathrm{m}/\mathrm{s}. $$Its acceleration versus time graph is given. Determine its velocity at $$t = 8.0\ \mathrm{s}.$$

Accepted Answer

$$51\ \mathrm{m}/\mathrm{s}$$

Question 13

A frictionless trolley follows a straight line path as shown in the figure. Which set of position, velocity, and acceleration graphs best represents the trolley's motion?

Accepted Answer

The first set (position increases non-linearly, velocity increases, acceleration is constant and positive)

Question 14

A vessel, measuring $$120\ \mathrm{m} in $$length, starts its uniform acceleration from a complete stop. When the front of the vessel reaches a buoy located $$300\ \mathrm{m}$$ away from its initial position, it is traveling at a speed of $$12\ \mathrm{m}/\mathrm{s}. $$What will be the speed of the rear end of the vessel as it passes the buoy?

Accepted Answer

$$20\ \mathrm{m}/\mathrm{s}$$

Question 15

An athlete tossed a ball vertically upward with a speed of $$v_1. A $$velocity sensor placed exactly $$3.0\ \mathrm{m}$$ above the point of release of the ball measures a speed of $$8.0\ \mathrm{m}/\mathrm{s}$$ when the ball is at the same horizontal level as the sensor and moving upward. Calculate $$v_1.$$

Accepted Answer

$$11\ \mathrm{m}/\mathrm{s}$$

Question 16

Two friends riding their respective bikes meet at a traffic signal and race to the next signal $$600\ \mathrm{m}$$ away. The red bike starts ahead of the black bike by $$2.0\ \mathrm{s}. $$The acceleration of the red bike is $$4.5\ \mathrm{m}/\mathrm{s}^2$$ which is smaller than the black bike's acceleration of $$5.5\ \mathrm{m}/\mathrm{s}^2. $$Determine who will reach the traffic light first.

Accepted Answer

Black bike

Question 17

A cyclist is accelerating up a $$25.0^\circ$$ incline with an acceleration of $$2.50\ \mathrm{m}/\mathrm{s}^2. $$Determine the horizontal component of their acceleration.

Accepted Answer

$$2.27\ \mathrm{m}/\mathrm{s}^2$$

Question 18

Calculate the magnitude and direction of $$\vec{M} = -3.0\hat{i} + 3.0\hat{j}. $$Which vector diagram correctly represents this vector?

Accepted Answer

The second image (vector points to the upper left, $$45^\circ$$ from the negative x-axis)

Question 19

James drives north for $$4.5\ \mathrm{km}$$, then $$2.8\ \mathrm{km}$$ west, and then $$1.3\ \mathrm{km}$$ south. Using the method of components, find the magnitude and direction of the resultant displacement.

Accepted Answer

Magnitude $$= 6.00\ \mathrm{km}$$, Direction $$= 48.8^\circ$$

Question 20

You are given two vectors $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and $$\vec{B} = 6\hat{i} + 8\hat{j}. $$Determine the direction of the vector difference $$\vec{B} - \vec{A}.$$

Accepted Answer

$$	heta = 53.13^\circ$$

Question 21

Vector $$\vec{M}$$ lies in the $$xy$$ plane making an angle of $$	heta$$ above the positive $$x-$$axis. Vector $$\vec{N} is $$lying in the same plane making an angle $$\Phi$$ below the positive $$x-$$axis. Determine their dot product.

Accepted Answer

$$MN(\cos	heta\cos\Phi + \sin	heta\sin\Phi)$$

Position-Time Graphs for an RC Car: Interpreting Motion Diagrams

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