Question 1

A swimmer swims at $$\vec{v}_{SW} = 2\,\mathrm{m/s} in $$still water. The river flows at $$\vec{v}_{WL} = 1\,\mathrm{m/s}$$ east. What is the swimmer's velocity relative to land if she swims directly north?

Accepted Answer

$$\vec{v}_{SL} = \sqrt{2^2$ + 1^2$} = 2.24\,\mathrm{m/s}$$, 26.6° east of north

Question 2

A ferryboat can cross a 1 km channel in 10 minutes on a calm day. If the current is $$4\,\mathrm{km/h}$$ east and the ferry's speed relative to water is $$6\,\mathrm{km/h}$$ north, how long does it take to cross from city X to Y?

Accepted Answer

$$t = \frac{1\,\mathrm{km}}{4.47\,\mathrm{km/h}} = 0.22\,\mathrm{h} (13 $$min)

Question 3

Which of the following best describes Newton's First Law?

Accepted Answer

An object at rest remains at rest, and an object in motion continues with constant velocity unless acted upon by a net external force.

Question 4

A 130 g spider hangs motionless from a thread at an angle of $$35^\circ to $$the vertical due to a breeze. What is the tension in the thread?

Accepted Answer

$$T = \frac{mg}{\cos(35^\circ)}$$

Question 5

Which of the following is NOT a fundamental force in nature?

Accepted Answer

Friction

Question 6

A block of mass $$2\,\mathrm{kg} is at $$rest on a frictionless incline. What is the normal force acting on the block if the incline makes an angle $$	heta$$ with the horizontal?

Accepted Answer

$$N = mg \cos 	heta$$

Question 7

You push two boxes down a rough hallway. What forces act on box A?

Accepted Answer

Normal force, gravitational force, friction force, and push force

Question 8

A block of mass $$m$$ slides down an incline with acceleration $$a. $$The friction force $$f$$ acting on the block is given by:

Accepted Answer

$$f = mg \sin 	heta - ma$$

Question 9

Which statement about static friction is correct?

Accepted Answer

Static friction opposes the intended motion and can vary up to a maximum value $$f_{s,\mathrm{max}} = \mu_s N$$

Question 10

A mass $$m = 50\,\mathrm{kg} is $$suspended by two strings at $$60^\circ$$ and $$30^\circ to $$the horizontal. What is the tension in the shorter string ($$T_1$$)?

Accepted Answer

$$T_1 = 424$$\,\mathrm{N}$$

Question 11

An 80 kg man rides an elevator. What is his apparent weight when the elevator descends with a constant acceleration of $$9.8\,\mathrm{m/s^2$}$$?

Accepted Answer

$$0\,\mathrm{N}$$

Question 12

Which of the following is a correct application of Newton's Third Law?

Accepted Answer

The force you exert on the ground while jumping is equal and opposite to the force the ground exerts on you.

Question 13

A paper airplane is launched at $$1.7\,\mathrm{m/s}$$ towards a wall $$3.0\,\mathrm{m}$$ away. A fan blows air at $$1.0\,\mathrm{m/s}$$ perpendicular to the plane's path. What is the resultant velocity of the plane?

Accepted Answer

$$v = \sqrt{1.7^2$ + 1.0^2$} = 1.97\,\mathrm{m/s}$$

Question 14

Which equation correctly expresses Newton's Second Law for multiple forces acting on an object?

Accepted Answer

$$\vec{F}_{net} = \sum \vec{F}_i = m\vec{a}$$

Question 15

A block of mass $$m is at $$rest on an incline with friction. Which force balances the component of gravity parallel to the incline?

Accepted Answer

Friction force

Question 16

When drawing a free body diagram (FBD), which of the following should NOT be included?

Accepted Answer

Forces caused by the object on other objects

Question 17

A block slides down a rough incline. Which direction does the friction force act?

Accepted Answer

Up the incline, opposing the motion

Question 18

Which of the following is the correct formula for the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by distance $$r$$?

Accepted Answer

$$F_g = G m_1$ m_2$ / r^2$

Question 19

A person stands on a level floor at rest. The normal force they experience is equal to their weight. This is a consequence of:

Accepted Answer

Newton's First Law

Lecture 3: Relative Velocity, Newton's Laws, Friction, and Free Body Diagrams

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