Q: A ball is thrown vertically upward with an initial velocity of $v_0 = 15\ \mathrm{m/s}$ from ground level. Neglecting air resistance, what is the maximum height the ball reaches? (Take $g = 9.80\ \mathrm{m/s^2}$.)

$h = \frac{v_0^2}{2g} = \frac{(15)^2}{2 \times 9.8} = 11.5\ \mathrm{m}$

Q: A rock is dropped from a cliff and hits the ground 2.0 seconds later. What is the height of the cliff? (Neglect air resistance, $g = 9.80\ \mathrm{m/s^2}$.)

$h = \frac{1}{2}gt^2 = \frac{1}{2} \times 9.8 \times (2.0)^2 = 19.6\ \mathrm{m}$

Q: A projectile is launched at an angle $\theta$ above the horizontal with initial speed $v_0$. Which of the following correctly gives the time of flight (total time in the air) if it lands at the same vertical level from which it was launched?

$t = \frac{2v_0 \sin\theta}{g}$

Q: A 5.0 kg box is pulled across a horizontal floor with a constant velocity by a force of 25 N applied at an angle of $30^\circ$ above the horizontal. The coefficient of kinetic friction between the box and the floor is closest to:

$\mu_k = \frac{25 \cos 30^\circ}{5.0 \times 9.8 - 25 \sin 30^\circ} \approx 0.59$

Q: A 2.0 kg block slides down a frictionless incline of height 3.0 m. What is its speed at the bottom?

$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 3.0} = 7.7\ \mathrm{m/s}$

Q: A 1.0 kg object is attached to a spring with spring constant $k = 200\ \mathrm{N/m}$ and is pulled so that the spring is stretched by 0.10 m. What is the potential energy stored in the spring?

$U = \frac{1}{2}kx^2 = \frac{1}{2} \times 200 \times (0.10)^2 = 1.0\ \mathrm{J}$

Q: A 10 kg crate is pushed up a $25^\circ$ frictionless incline at constant speed. What is the magnitude of the force parallel to the incline required to move the crate?

$F = mg \sin \theta = 10 \times 9.8 \times \sin 25^\circ \approx 41.4\ \mathrm{N}$

Q: A 0.5 kg ball is dropped from a height of 10 m. What is its speed just before it hits the ground? (Neglect air resistance.)

$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$

Q: A 3.0 kg object is moving at 4.0 m/s. What is its kinetic energy?

$K = \frac{1}{2}mv^2 = \frac{1}{2} \times 3.0 \times (4.0)^2 = 24\ \mathrm{J}$

Q: A 1.5 kg block is attached to a light string and hangs over a frictionless pulley, connected to a 2.5 kg block resting on a table. If the system is released from rest, what is the acceleration of the blocks? (Neglect friction.)

$a = \frac{m_1g}{m_1 + m_2} = \frac{1.5 \times 9.8}{1.5 + 2.5} = 3.7\ \mathrm{m/s^2}$

Question 1

A ball is thrown vertically upward with an initial velocity of $v_0 = 15\ \mathrm{m/s}$ from ground level. Neglecting air resistance, what is the maximum height the ball reaches? (Take $g = 9.80\ \mathrm{m/s^2}$.)

Accepted Answer

$h = \frac{v_0^2}{2g} = \frac{(15)^2}{2 	imes 9.8} = 11.5\ \mathrm{m}$

Question 2

A rock is dropped from a cliff and hits the ground 2.0 seconds later. What is the height of the cliff? (Neglect air resistance, $g = 9.80\ \mathrm{m/s^2}$.)

Accepted Answer

$h = \frac{1}{2}gt^2 = \frac{1}{2} 	imes 9.8 	imes (2.0)^2 = 19.6\ \mathrm{m}$

Question 3

A projectile is launched at an angle $	heta$ above the horizontal with initial speed $v_0$. Which of the following correctly gives the time of flight (total time in the air) if it lands at the same vertical level from which it was launched?

Accepted Answer

$t = \frac{2v_0 \sin	heta}{g}$

Question 4

A 5.0 kg box is pulled across a horizontal floor with a constant velocity by a force of 25 N applied at an angle of $30^\circ$ above the horizontal. The coefficient of kinetic friction between the box and the floor is closest to:

Accepted Answer

$\mu_k = \frac{25 \cos 30^\circ}{5.0 	imes 9.8 - 25 \sin 30^\circ} \approx 0.59$

Question 5

A 2.0 kg block slides down a frictionless incline of height 3.0 m. What is its speed at the bottom?

Accepted Answer

$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 3.0} = 7.7\ \mathrm{m/s}$

Question 6

A 1.0 kg object is attached to a spring with spring constant $k = 200\ \mathrm{N/m}$ and is pulled so that the spring is stretched by 0.10 m. What is the potential energy stored in the spring?

Accepted Answer

$U = \frac{1}{2}kx^2 = \frac{1}{2} 	imes 200 	imes (0.10)^2 = 1.0\ \mathrm{J}$

Question 7

A 10 kg crate is pushed up a $25^\circ$ frictionless incline at constant speed. What is the magnitude of the force parallel to the incline required to move the crate?

Accepted Answer

$F = mg \sin 	heta = 10 	imes 9.8 	imes \sin 25^\circ \approx 41.4\ \mathrm{N}$

Question 8

A 0.5 kg ball is dropped from a height of 10 m. What is its speed just before it hits the ground? (Neglect air resistance.)

Accepted Answer

$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ \mathrm{m/s}$

Question 9

A 3.0 kg object is moving at 4.0 m/s. What is its kinetic energy?

Accepted Answer

$K = \frac{1}{2}mv^2 = \frac{1}{2} 	imes 3.0 	imes (4.0)^2 = 24\ \mathrm{J}$

Question 10

A 1.5 kg block is attached to a light string and hangs over a frictionless pulley, connected to a 2.5 kg block resting on a table. If the system is released from rest, what is the acceleration of the blocks? (Neglect friction.)

Accepted Answer

$a = \frac{m_1g}{m_1 + m_2} = \frac{1.5 	imes 9.8}{1.5 + 2.5} = 3.7\ \mathrm{m/s^2}$

Question 11

A 60 kg skier starts from rest at the top of a 20 m high hill. If there is no friction, what is her speed at the bottom?

Accepted Answer

$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} = 19.8\ \mathrm{m/s}$

Question 12

A 1000 kg car accelerates from rest to 20 m/s in 10 seconds. What is the average power delivered to the car during this time?

Accepted Answer

$P = \frac{\Delta K}{t} = \frac{\frac{1}{2}mv^2}{t} = \frac{0.5 	imes 1000 	imes 400}{10} = 20,000\ \mathrm{W}$

Question 13

A 2.0 kg block is pushed against a spring (spring constant $k = 400\ \mathrm{N/m}$) compressing it by 0.05 m. The block is then released from rest. What is its speed as it leaves the spring (on a frictionless surface)?

Accepted Answer

$v = \sqrt{\frac{kx^2}{m}} = \sqrt{\frac{400 	imes (0.05)^2}{2.0}} = 1.0\ \mathrm{m/s}$

Question 14

A 50 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40. What is the minimum horizontal force required to start moving the box?

Accepted Answer

$F = \mu_s N = 0.40 	imes 50 	imes 9.8 = 196\ \mathrm{N}$

Question 15

A 0.2 kg ball is thrown horizontally from a 10 m high table with a speed of 5 m/s. How far from the base of the table does the ball land? (Neglect air resistance.)

Accepted Answer

$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 10}{9.8}} = 1.43\ \mathrm{s}$; $x = v_xt = 5 	imes 1.43 = 7.15\ \mathrm{m}$

Question 16

A 70 kg person runs up a 3.0 m high flight of stairs in 2.5 seconds. What is the average power output?

Accepted Answer

$P = \frac{mgh}{t} = \frac{70 	imes 9.8 	imes 3.0}{2.5} = 823\ \mathrm{W}$

Question 17

A 1.0 kg object is moving in a circle of radius 2.0 m at a constant speed of 3.0 m/s. What is the magnitude of the net force acting on the object?

Accepted Answer

$F = \frac{mv^2}{r} = \frac{1.0 	imes 9}{2.0} = 4.5\ \mathrm{N}$

Free-Falling Objects and Acceleration Due to Gravity

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