Q: A vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 4. $$What is the magnitude and direction (angle from the positive $$x-$$axis) of $$\vec{A}$$?

$$|\vec{A}| = 5,\ \theta = 126.9^\circ$$

Q: A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height it reaches above the launch point?

$$h = \frac{v_0$^2}{2g} = \frac{(20)^2$}{2 \times 9.8} = 20.4\ \mathrm{m}$$

Q: A 2.0 kg block is pulled across a horizontal surface with a force of $$10\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$0.2$$, what is the acceleration of the block?

$$a = \frac{10 \cos 30^\circ - 0.2 (2.0 \times 9.8 - 10 \sin 30^\circ)}{2.0} = 3.1\ \mathrm{m/s}^2$$

Q: A cyclist rounds a flat curve of radius $$25\ \mathrm{m} at a $$speed of $$10\ \mathrm{m/s}. $$What is the minimum coefficient of static friction required to prevent slipping?

$$\mu_s = \frac{v^2$}{gR} = \frac{(10)^2$}{9.8 \times 25} = 0.41$$

Q: A 5.0 kg box rests on a 30$$^\circ$$ incline. What is the magnitude of the normal force exerted by the incline on the box?

$$F_N = mg \cos \theta = 5.0 \times 9.8 \times \cos 30^\circ = 42.4\ \mathrm{N}$$

Q: A 3.0 kg object moves in a circle of radius $$2.0\ \mathrm{m} at a $$constant speed of $$4.0\ \mathrm{m/s}. $$What is the magnitude of the net force acting on the object?

$$F = m \frac{v^2$}{R} = 3.0 \times \frac{16}{2.0} = 24\ \mathrm{N}$$

Q: A 10 kg box is at rest on a horizontal floor. The coefficient of static friction is $$0.5. $$What is the maximum horizontal force that can be applied before the box starts to move?

$$F_{\text{max}} = \mu_s F_N = 0.5 \times 10 \times 9.8 = 49\ \mathrm{N}$$

Q: A 2.0 kg block is connected by a light string over a frictionless pulley to a 3.0 kg block hanging vertically. The 2.0 kg block rests on a frictionless table. What is the acceleration of the system after release?

$$a = \frac{m_2$ g}{m_1$ + m_2$} = \frac{3.0 \times 9.8}{2.0 + 3.0} = 5.88\ \mathrm{m/s}^2$$

Q: A projectile is launched from ground level at $$v_0 = 20$$\ \mathrm{m/s}$$ at an angle of 30$$^\circ$$ above the horizontal. What is the range of the projectile (neglect air resistance)?

$$R = \frac{v_0$^2 \sin 2\theta}{g} = \frac{400 \times \sin 60^\circ}{9.8} = 35.4\ \mathrm{m}$$

Question 1

A car travels 120 km in 2.0 hours, then 80 km in 1.0 hour. What is the car's average speed for the entire trip?

Accepted Answer

$$\frac{120\ \mathrm{km} + 80\ \mathrm{km}}{2.0\ \mathrm{h} + 1.0\ \mathrm{h}} = 66.7\ \mathrm{km/h}$$

Question 2

A vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 4. $$What is the magnitude and direction (angle from the positive $$x-$$axis) of $$\vec{A}$$?

Accepted Answer

$$|\vec{A}| = 5,\ 	heta = 126.9^\circ$$

Question 3

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height it reaches above the launch point?

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(20)^2$}{2 	imes 9.8} = 20.4\ \mathrm{m}$$

Question 4

A 2.0 kg block is pulled across a horizontal surface with a force of $$10\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$0.2$$, what is the acceleration of the block?

Accepted Answer

$$a = \frac{10 \cos 30^\circ - 0.2 (2.0 	imes 9.8 - 10 \sin 30^\circ)}{2.0} = 3.1\ \mathrm{m/s}^2$$

Question 5

A cyclist rounds a flat curve of radius $$25\ \mathrm{m} at a $$speed of $$10\ \mathrm{m/s}. $$What is the minimum coefficient of static friction required to prevent slipping?

Accepted Answer

$$\mu_s = \frac{v^2$}{gR} = \frac{(10)^2$}{9.8 	imes 25} = 0.41$$

Question 6

A 5.0 kg box rests on a 30$$^\circ$$ incline. What is the magnitude of the normal force exerted by the incline on the box?

Accepted Answer

$$F_N = mg \cos 	heta = 5.0 	imes 9.8 	imes \cos 30^\circ = 42.4\ \mathrm{N}$$

Question 7

A 3.0 kg object moves in a circle of radius $$2.0\ \mathrm{m} at a $$constant speed of $$4.0\ \mathrm{m/s}. $$What is the magnitude of the net force acting on the object?

Accepted Answer

$$F = m \frac{v^2$}{R} = 3.0 	imes \frac{16}{2.0} = 24\ \mathrm{N}$$

Question 8

A 10 kg box is at rest on a horizontal floor. The coefficient of static friction is $$0.5. $$What is the maximum horizontal force that can be applied before the box starts to move?

Accepted Answer

$$F_{	ext{max}} = \mu_s F_N = 0.5 	imes 10 	imes 9.8 = 49\ \mathrm{N}$$

Question 9

A 2.0 kg block is connected by a light string over a frictionless pulley to a 3.0 kg block hanging vertically. The 2.0 kg block rests on a frictionless table. What is the acceleration of the system after release?

Accepted Answer

$$a = \frac{m_2$ g}{m_1$ + m_2$} = \frac{3.0 	imes 9.8}{2.0 + 3.0} = 5.88\ \mathrm{m/s}^2$$

Question 10

A projectile is launched from ground level at $$v_0 = 20$$\ \mathrm{m/s}$$ at an angle of 30$$^\circ$$ above the horizontal. What is the range of the projectile (neglect air resistance)?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g} = \frac{400 	imes \sin 60^\circ}{9.8} = 35.4\ \mathrm{m}$$

Question 11

A 1.0 kg object is suspended from a scale in an elevator accelerating upward at $$2.0\ \mathrm{m/s}^2. $$What does the scale read?

Accepted Answer

$$F_N = m(g + a) = 1.0 	imes (9.8 + 2.0) = 11.8\ \mathrm{N}$$

Question 12

A 2.0 kg block slides down a 25$$^\circ$$ incline at constant velocity. What is the coefficient of kinetic friction between the block and the incline?

Accepted Answer

$$\mu_k = 	an 25^\circ = 0.47$$

Question 13

A 0.5 kg ball is swung in a horizontal circle of radius 1.5 m at a constant speed. If the tension in the string is 6.0 N, what is the speed of the ball?

Accepted Answer

$$v = \sqrt{\frac{F_T R}{m}} = \sqrt{\frac{6.0 	imes 1.5}{0.5}} = 4.24\ \mathrm{m/s}$$

Question 14

A 1.0 kg block is pressed against a vertical wall by a horizontal force of 20 N. If the coefficient of static friction is 0.6, what is the maximum weight the friction can support before the block slips?

Accepted Answer

$$F_{s,	ext{max}} = \mu_s F_N = 0.6 	imes 20 = 12\ \mathrm{N}$$

Question 15

A 2.0 kg block is at rest on a horizontal table. A horizontal force of 3.0 N is applied, but the block does not move. If the coefficient of static friction is 0.4, what is the magnitude of the friction force acting on the block?

Accepted Answer

$$F_s = 3.0\ \mathrm{N}$$

Question 16

A 1.5 kg object moves in a circle of radius 0.75 m at a constant speed. If it completes one revolution in 2.0 s, what is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{v^2$}{R} = \frac{(2\pi R / T)^2$}{R} = \frac{(2\pi 	imes 0.75 / 2.0)^2$}{0.75} = 5.55\ \mathrm{m/s}^2$$

Question 17

A 2.0 kg block is pulled up a rough incline (angle $$30^\circ) at $$constant speed. The coefficient of kinetic friction is 0.3. What is the magnitude of the pulling force parallel to the incline?

Accepted Answer

$$F = mg \sin 	heta + \mu_k mg \cos 	heta = 2.0 	imes 9.8 	imes \sin 30^\circ + 0.3 	imes 2.0 	imes 9.8 	imes \cos 30^\circ = 9.8 + 5.1 = 14.9\ \mathrm{N}$$

Question 18

A 1.0 kg object is moving with velocity $$\vec{v}_1 = (2.0\ \hat{\imath} + 3.0\ \hat{\jmath})\ \mathrm{m/s}$$ and is acted on by a constant force $$\vec{F} = (4.0\ \hat{\imath} - 2.0\ \hat{\jmath})\ \mathrm{N}$$ for 2.0 s. What is the final velocity?

Accepted Answer

$$\vec{v}_2 = \vec{v}_1 + \frac{\vec{F}}{m} t = (2.0 + 8.0)\ \hat{\imath} + (3.0 - 4.0)\ \hat{\jmath} = (10.0\ \hat{\imath} - 1.0\ \hat{\jmath})\ \mathrm{m/s}$$

Question 19

A 2.0 kg block is attached to a rope that passes over a frictionless pulley and is connected to a 3.0 kg block hanging vertically. The coefficient of kinetic friction between the 2.0 kg block and the table is 0.1. What is the acceleration of the system after release?

Accepted Answer

$$a = \frac{m_2$ g - \mu_k m_1$ g}{m_1$ + m_2$} = \frac{3.0 	imes 9.8 - 0.1 	imes 2.0 	imes 9.8}{2.0 + 3.0} = \frac{29.4 - 1.96}{5.0} = 5.5\ \mathrm{m/s}^2$$

PHYS 206 Exam 1 Review: Chapters 1–5 Study Guide

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