Exam 2 Review

2D Motion

100

What must a motion have to be two-dimensional? 

Two components(typically x and y).

200

How do you graphically add AND subtract vectors?

Addition: After drawing the first vector, begin drawing the second vector from the arrow tip of the first.

Subtraction: After drawing the first vector, begin drawing the second vector from the tail of the first vector, AND flipping the second vector. 

300

What is the magnitude of a vector?

r² = r_x² + r_y² 

400

If a jogger travels 100 meters 20^o North of due East, and he needs to at least travel 75 meters North, will he accomplish his requirement?

No, the jogger will not accomplish his requirement.

y = r*sin(theta)

y = 100*sin(20^o)

y = 34.20 m

34.20 m < 75 m

500

A bat flies 30^o South of due East for 50 meters, then flies 45^o North of due West for 65 meters. What is the bat's displacement vector?

r_1,y = 50*sin(30^o) = 25 m, r_1,x = 50*cos(30^o) = 43.3 m

r₁ = (43.3, -25)

r_2,y = 65*sin(45^o) = 45.96 m, r_2,x = 65*cos(45^o) = 45.96

r₂ = (-45.96, 45.96)

r_tot = r₁ + r₂ = (43.3, -25) + (-45.96, 45.96) = (-2.7, 21.0)

Newton's Laws

100

What is Newton's First Law of Motion?

The Law of Inertia: An object in motion stays in motion, and an object at rest stays at rest unless acted upon by an outside force. 

200

What is Newton's Second Law of Motion?

F = ma

300

What is Newton's Third Law of Motion?

Every action has an equal and opposite reaction. 

400

If an object with a mass of 10 kg was thrown off a building, how much force would it have when it hits the ground?

F = ma

F = (10 kg)(-9.8 m/s²)

F = -98 N or 98 N down into the ground

500

If I am standing on ice, and I apply a 100 N force on the wall, and I have a mass of 92 kg, how much will my initial acceleration be after pushing off the wall? Will I continue at this acceleration?

F = ma -> a = F/m

a = (-100 N)/(92 kg) = -1.09 m/s²

After pushing off the wall, I will not continue to accelerate because I am no longer applying a force, and therefore no force is being applied to be. 

Drawing Free Body Diagrams

100

A ball sitting on a table. 

Up: Normal Force 

Down: Force of gravity

Up and Down Forces cancel. 

200

A book sitting on a table, under another book. 

Up: Normal Force of the table

Down: Force of gravity, Force of above book on the below book

Up force = Sum of Down Forces

300

A ball in free fall that has not reached terminal velocity(still accelerating down).

Up: Air resistance

Down: Gravity

Down force overcomes as acceleration is down

400

A car on the road moving at a constant speed.

Up: Normal Force of the road

Down: Force of gravity

Right: Force applied to accelerate the car forward

Left: Friction

Up and down forces cancel and Right and Left forces cancel. 

500

A shopping cart accelerating forward. 

Up: Normal Force of the ground

Down: Force of gravity on the cart

Left: Force of Friction

Right: Force applied by the pusher

Up and Down forces cancel. Right force overcomes left force. 

Forces

100

Force of a falling object due to Earth

Force of Gravity

200

Force applied by a tight string or rope

Tension Force

300

Force of two objects rubbing together

Friction Force

400

General force given to the system

Applied Force

500

Force applied by two objects touching, acting perpendicular to the surface.

Normal Force

Problem Solving

100

A textbook is sitting on a table and its mass is 5 kg. What is the normal force applied by the table?

F_N = -mg 

= -(5 kg)(-9.8 m/s²)

= 49 N

200

A block with a mass of 10 kg is pulled against the ground with 20 N. The block is moving at a constant speed. What is the counteracting friction force?

F_Net = 0.

F_Applied + F_f = 0

F_f = -F_Applied

F_f = -(20 N)

= -20 N

300

I am pulling a wagon with a string where it's moving at a constant speed. If the force of friction acting on the wagon is 35 N, and I am pulling the string at 35^o from parallel, at what force am I pulling the string?

F_T,x = -F_f = -(-35 N) = +35 N

F_T,x = F_T*cos(theta) -> F_T = F_T,x/cos(theta)

F_T = (35 N)/cos(35^o) 

= 42.7 N

400

If a ball with a mass of 5 kg is accelerating across the floor at 2 m/s², and the floor causes a friction force of 20 N, what is the net force on the ball? What is the applied force on the ball?

F_Net = ma = (5 kg)(2 m/s²) = 10 N

F_Net = F_Applied + F_f -> F_Applied = F_Net - F_f

= 10 N - (-20 N)

= 30 N

500

If an object with a mass of 4 kg initially starts at rest, and I apply a constant 5 N force on the object for 10 seconds, how far will the object travel?

F = ma -> a = F/m

x_f = x_i + v_it + 1/2(a)(t²)

x_f = 0 + (0)(10 s) + 1/2(5 N/4 kg)(10²)

x_f = 62.5 m

The object travels 62.5 meters.