Q: A typical multivitamin tablet contains 2 mg of vitamin B2 (riboflavin), and the recommended daily allowance (RDA) is 0.0030 g/day. How many tablets should a person take each day to get the proper amount of this vitamin, assuming the rest comes from no other sources?

$$\frac{0.0030\ \text{g}}{0.002\ \text{g}} = 1.5$$ tablets

Q: A crate with mass $$32.5\ \text{kg} is $$initially at rest on a warehouse floor and is acted on by a net horizontal force of $$140\ \text{N}. $$What is the acceleration produced?

$$a = \frac{140}{32.5} = 4.31\ \text{m/s}^2$$

Q: A juggler throws a bowling pin straight up with an initial speed of $$8.20\ \text{m/s}. $$How much time elapses until the bowling pin returns to the juggler’s hand?

$$t = \frac{2v_0}{g} = \frac{2 \times 8.20}{9.8} = 1.67\ \text{s}$$

Q: You walk 60.0 m due east to your windmill, then turn around and slowly walk 40.0 m west to a bench where you sit and watch the sunset. What is your net displacement from your house to the bench?

$$60.0\ \text{m} - 40.0\ \text{m} = 20.0\ \text{m}$$ east

Q: A cat walks in a straight line, and its position as a function of time is given by $$x(t) = 3.0t^2$ + 2.0t + 1.0 (in $$meters, $$t in $$seconds). What is the cat’s acceleration?

$$a = \frac{d^2$x}{dt^2$} = 6.0\ \text{m/s}^2$$

Q: You drop a $$2.00\ \text{kg}$$ book to a friend who stands on the ground at distance $$D = 10.0\ \text{m}$$ below. If your friend’s outstretched hands are at distance $$d = 1.50\ \text{m}$$ above the ground, what is the gravitational potential energy $$U of $$the book when it is released?

$$U = mgh = 2.00 \times 9.8 \times 10.0 = 196\ \text{J}$$

Q: A crate with mass $$32.5\ \text{kg} is $$acted on by a net horizontal force of $$140\ \text{N}$$ for $$10.0\ \text{s}. $$What is its speed at the end of $$10.0\ \text{s}$$?

$$v = at = \left(\frac{140}{32.5}\right) \times 10.0 = 43.1\ \text{m/s}$$

Q: Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in the figure. If the $$x-$$components of the three pulls are $$411\ \text{N}$$, $$902\ \text{N}$$, and $$722\ \text{N}$$, what is the magnitude of the resultant force in the $$x-$$direction?

$$F_x = 411 + 902 + 722 = 2035\ \text{N}$$

Q: A person walks from their house to a windmill $$60.0\ \text{m}$$ east, then $$40.0\ \text{m}$$ west to a bench. If the entire trip takes $$80.0\ \text{s}$$, what is their average velocity?

$$v_{avg} = \frac{20.0}{80.0} = 0.25\ \text{m/s}$$\ east

Q: If the gravitational potential energy $$U of a $$system is taken to be zero at ground level, what is $$U$$ when a $$2.00\ \text{kg}$$ book is at height $$h = 1.50\ \text{m}$$ above the ground?

$$U = mgh = 2.00 \times 9.8 \times 1.50 = 29.4\ \text{J}$$

Question 1

A typical multivitamin tablet contains 2 mg of vitamin B2 (riboflavin), and the recommended daily allowance (RDA) is 0.0030 g/day. How many tablets should a person take each day to get the proper amount of this vitamin, assuming the rest comes from no other sources?

Accepted Answer

$$\frac{0.0030\ 	ext{g}}{0.002\ 	ext{g}} = 1.5$$ tablets

Question 2

A crate with mass $$32.5\ 	ext{kg} is $$initially at rest on a warehouse floor and is acted on by a net horizontal force of $$140\ 	ext{N}. $$What is the acceleration produced?

Accepted Answer

$$a = \frac{140}{32.5} = 4.31\ 	ext{m/s}^2$$

Question 3

A juggler throws a bowling pin straight up with an initial speed of $$8.20\ 	ext{m/s}. $$How much time elapses until the bowling pin returns to the juggler’s hand?

Accepted Answer

$$t = \frac{2v_0}{g} = \frac{2 	imes 8.20}{9.8} = 1.67\ 	ext{s}$$

Question 4

You walk 60.0 m due east to your windmill, then turn around and slowly walk 40.0 m west to a bench where you sit and watch the sunset. What is your net displacement from your house to the bench?

Accepted Answer

$$60.0\ 	ext{m} - 40.0\ 	ext{m} = 20.0\ 	ext{m}$$ east

Question 5

A cat walks in a straight line, and its position as a function of time is given by $$x(t) = 3.0t^2$ + 2.0t + 1.0 (in $$meters, $$t in $$seconds). What is the cat’s acceleration?

Accepted Answer

$$a = \frac{d^2$x}{dt^2$} = 6.0\ 	ext{m/s}^2$$

Question 6

A patient must wear a strap that produces an upward force of $$5.00\ 	ext{N} on $$his chin. The tension is the same throughout the strap. What tension must the strap be adjusted to provide the necessary upward force?

Accepted Answer

$$T = 5.00\ 	ext{N}$$

Question 7

You drop a $$2.00\ 	ext{kg}$$ book to a friend who stands on the ground at distance $$D = 10.0\ 	ext{m}$$ below. If your friend’s outstretched hands are at distance $$d = 1.50\ 	ext{m}$$ above the ground, what is the gravitational potential energy $$U of $$the book when it is released?

Accepted Answer

$$U = mgh = 2.00 	imes 9.8 	imes 10.0 = 196\ 	ext{J}$$

Question 8

A crate with mass $$32.5\ 	ext{kg} is $$acted on by a net horizontal force of $$140\ 	ext{N}$$ for $$10.0\ 	ext{s}. $$What is its speed at the end of $$10.0\ 	ext{s}$$?

Accepted Answer

$$v = at = \left(\frac{140}{32.5}ight) 	imes 10.0 = 43.1\ 	ext{m/s}$$

Question 9

Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in the figure. If the $$x-$$components of the three pulls are $$411\ 	ext{N}$$, $$902\ 	ext{N}$$, and $$722\ 	ext{N}$$, what is the magnitude of the resultant force in the $$x-$$direction?

Accepted Answer

$$F_x = 411 + 902 + 722 = 2035\ 	ext{N}$$

Question 10

A person walks from their house to a windmill $$60.0\ 	ext{m}$$ east, then $$40.0\ 	ext{m}$$ west to a bench. If the entire trip takes $$80.0\ 	ext{s}$$, what is their average velocity?

Accepted Answer

$$v_{avg} = \frac{20.0}{80.0} = 0.25\ 	ext{m/s}$$\ east

Question 11

If the gravitational potential energy $$U of a $$system is taken to be zero at ground level, what is $$U$$ when a $$2.00\ 	ext{kg}$$ book is at height $$h = 1.50\ 	ext{m}$$ above the ground?

Accepted Answer

$$U = mgh = 2.00 	imes 9.8 	imes 1.50 = 29.4\ 	ext{J}$$

Question 12

A cat’s position is given by $$x(t) = 3.0t^2$ + 2.0t + 1.0. $$What is the cat’s velocity at $$t = 5.0\ 	ext{s}$$?

Accepted Answer

$$v = \frac{dx}{dt} = 6.0t + 2.0 = 6.0 	imes 5.0 + 2.0 = 32.0\ 	ext{m/s}$$

Question 13

A person walks $$60.0\ 	ext{m}$$ east, then $$40.0\ 	ext{m}$$ west, and finally $$36.0\ 	ext{m}$$ south. What is the magnitude of their net displacement from the starting point?

Accepted Answer

$$\sqrt{(60.0 - 40.0)^2$ + 36.0^2$} = \sqrt{400 + 1296} = \sqrt{1696} = 41.2\ 	ext{m}$$

Question 14

A $$2.00\ 	ext{kg}$$ book is dropped from a height of $$10.0\ 	ext{m}$$ above the ground. What is its speed just before it reaches the ground? (Assume $$g = 9.8\ 	ext{m/s}^2$$ and neglect air resistance.)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10.0} = 14.0\ 	ext{m/s}$$

Question 15

A patient must wear a strap that produces an upward force of $$5.00\ 	ext{N} on $$his chin. If the strap is at an angle of $$30^\circ to $$the vertical, what tension must the strap be adjusted to provide the necessary upward force?

Accepted Answer

$$T = \frac{5.00}{\cos 30^\circ} = 5.77\ 	ext{N}$$

Question 16

A crate with mass $$32.5\ 	ext{kg} is $$acted on by a net horizontal force of $$140\ 	ext{N}$$ for $$10.0\ 	ext{s}. $$How far does the crate travel in $$10.0\ 	ext{s}$$?

Accepted Answer

$$x = \frac{1}{2}at^2$ = \frac{1}{2} 	imes \frac{140}{32.5} 	imes (10.0)^2$ = 215.5\ 	ext{m}$$

Question 17

A cat’s position is given by $$x(t) = 3.0t^2$ + 2.0t + 1.0. $$What is the cat’s displacement during the first $$4.5\ 	ext{s}$$?

Accepted Answer

$$x(4.5) - x(0) = [3.0 	imes (4.5)^2$ + 2.0 	imes 4.5 + 1.0] - 1.0 = 60.75 + 9.0 + 1.0 - 1.0 = 69.75\ 	ext{m}$$

Mechanics Study Guide: Problem-Solving in Introductory Physics

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