Q: A 5 kg object is dropped from rest from a height of 50 m. Neglecting air resistance, what is its velocity just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 50} \approx 31.3\ \mathrm{m/s}$$

Q: A block of mass $$m is $$sliding down a frictionless incline of angle $$\theta. $$What is the equation for its position along the incline as a function of time, starting from rest?

$$x(t) = \frac{1}{2}g \sin \theta\ t^2$

Question 1

Which of the following best describes the difference between kinematics and dynamics in physics?

Accepted Answer

Kinematics describes motion without regard to its causes, while dynamics studies the forces that cause motion.

Question 2

According to Newton's second law, if the net force on an object is zero, what can be said about the object's velocity?

Accepted Answer

The object must be moving at a constant speed in a straight line.

Question 3

A 2 kg block slides down a frictionless incline at an angle $$	heta = 30^\circ to $$the horizontal. What is the magnitude of its acceleration down the slope?

Accepted Answer

$$g \sin 30^\circ$$

Question 4

If the gravitational force on an object is $$F = mg$$ and Newton's second law is $$F = ma$$, what does this imply about the acceleration of all objects in free fall near Earth's surface (neglecting air resistance)?

Accepted Answer

The acceleration is equal to $$g$$ for all objects, regardless of mass.

Question 5

A block of mass $$m is on a $$frictionless incline of angle $$	heta. $$What is the normal force $$N$$ exerted by the incline on the block?

Accepted Answer

$$N = mg \cos 	heta$$

Question 6

Two blocks, $$A ($$mass $$M) on a $$frictionless table and $$B ($$mass $$m) $$hanging off the edge, are connected by a light string over a frictionless pulley. What is the acceleration of the system?

Accepted Answer

$$a = \dfrac{mg}{M + m}$$

Question 7

A block of mass $$m is $$pulled up a frictionless incline at angle $$	heta by a $$force $$F$$ parallel to the incline. What is the net force on the block along the incline?

Accepted Answer

$$F - mg \sin 	heta$$

Question 8

A 5 kg object is dropped from rest from a height of 50 m. Neglecting air resistance, what is its velocity just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 50} \approx 31.3\ \mathrm{m/s}$$

Question 9

If a block is sliding down a frictionless incline and the angle of the incline is increased, what happens to the acceleration of the block?

Accepted Answer

The acceleration increases.

Question 10

A block of mass $$m is at $$rest on a horizontal frictionless surface. A force $$F is $$applied at an angle $$\phi$$ above the horizontal. What is the vertical component of the force?

Accepted Answer

$$F \sin \phi$$

Question 11

Two blocks are connected by a string over a frictionless pulley. If a parachute applies an upward force of $$F = mg/2 to $$the hanging block, how does this affect the acceleration of the system?

Accepted Answer

The acceleration is halved compared to the case without the parachute.

Question 12

Which of the following statements is a correct application of Newton's third law?

Accepted Answer

The force of the Earth pulling on an apple is equal in magnitude and opposite in direction to the force of the apple pulling on the Earth.

Question 13

A block of mass $$m is $$sliding down a frictionless incline of angle $$	heta. $$What is the equation for its position along the incline as a function of time, starting from rest?

Accepted Answer

$$x(t) = \frac{1}{2}g \sin 	heta\ t^2$

Question 14

A block is pulled horizontally on a frictionless surface with a force $$F. If $$the block has mass $$m$$, what is its acceleration?

Accepted Answer

$$a = F/m$$

Question 15

A 10 kg box is at rest on a frictionless table. A horizontal force of 20 N is applied. What is the acceleration of the box?

Accepted Answer

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

Question 16

A block of mass $$m is on a $$frictionless incline. If the incline is tilted to $$90^\circ$$, what is the acceleration of the block?

Accepted Answer

$$a = g$$

Question 17

A block is pulled by a force $$F at an $$angle $$	heta$$ above the horizontal on a frictionless surface. What is the horizontal component of the force?

Accepted Answer

$$F \cos 	heta$$

Question 18

If the net force on a 3 kg object is $$12\ \mathrm{N}$$, what is its acceleration?

Accepted Answer

$$4\ \mathrm{m/s^2$}$$

Newton's Second Law and Applications: Inclined Planes and Connected Objects

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