AP Physics Unit

Unit 2 - Linear Forces

Intermediate

Conceptual

GQ

An object has a mass of 10 kg. For each case below answer the questions and provide an example.

  1. If an object is moving, is it possible for the net force acting on it to be zero?
  2. If the acceleration of an object is zero, are no forces acting on it?
  3. Only one force acts on an object. Can the object have zero acceleration?
  4. Only one force acts on an object. Can it have zero velocity?

  1. Yes. An car that is traveling at a constant speed will have a net force of 0.
  2. No. Right now your acceleration is 0, but you still have gravitational and normal forces acting on your body.
  3. No. It cannot have 0 acceleration. A singular force is a net force, thus will always cause an acceleration, like a booster propelling a rocket in space.
  4. Yes. Throwing a ball vertically will show that the ball reaches 0 velocity at the top, while only one force (force of gravity) act on it throughout the motion of the ball.

1. Object Moving with Net Force Zero

Question:

If an object is moving, is it possible for the net force acting on it to be zero?

Answer

Yes, it is possible.

Explanation Example
When an object moves with constant velocity (including zero acceleration), the net force acting on it is zero. This is in accordance with Newton’s First Law of Motion, which states that an object in motion will remain in motion at a constant velocity unless acted upon by a net external force. A 10 kg object sliding on a frictionless surface at a constant speed.

2. Object with Zero Acceleration

Question:

If the acceleration of an object is zero, are no forces acting on it?

Answer:

No, it’s not necessarily true that no forces are acting on it.

Explanation Example
Zero acceleration means that the net force is zero, but it does not imply that no forces are acting on the object. It could be that multiple forces are acting on it, but they are balanced, resulting in no net force and thus no acceleration. A 10 kg object at rest on a horizontal surface with gravitational force downward balanced by the normal force upward.

3. Single Force and Zero Acceleration

Question:

Only one force acts on an object. Can the object have zero acceleration?

Answer:

No, if only one force acts on an object, the object cannot have zero acceleration.

Explanation Example
If a single unbalanced force acts on an object, it will cause the object to accelerate in the direction of the force, in accordance with Newton’s Second Law of Motion. A 10 kg object in free fall under the influence of gravity alone.

4. Single Force and Zero Velocity

Question:

Only one force acts on an object. Can it have zero velocity?

Answer:

Yes, it can have zero velocity at a specific moment.

Explanation Example
An object can have zero velocity at a particular instant, especially at the turning point in its motion, even if a single force is acting on it. However, it will not remain at zero velocity if the force continues to act. A 10 kg object thrown vertically upward will have zero velocity at the highest point of its trajectory, before starting to fall back down.

Each of these examples demonstrates different aspects of Newton’s Laws of Motion and the relationship between forces, velocity, and acceleration.

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  1. Yes. An car that is traveling at a constant speed will have a net force of 0.
  2. No. Right now your acceleration is 0, but you still have gravitational and normal forces acting on your body.
  3. No. It cannot have 0 acceleration. A singular force is a net force, thus will always cause an acceleration, like a booster propelling a rocket in space.
  4. Yes. Throwing a ball vertically will show that the ball reaches 0 velocity at the top, while only one force (force of gravity) act on it throughout the motion of the ball.

Nerd Notes

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KinematicsForces
\Delta x = v_i t + \frac{1}{2} at^2F = ma
v = v_i + atF_g = \frac{G m_1m_2}{r^2}
a = \frac{\Delta v}{\Delta t}f = \mu N
R = \frac{v_i^2 \sin(2\theta)}{g} 
Circular MotionEnergy
F_c = \frac{mv^2}{r}KE = \frac{1}{2} mv^2
a_c = \frac{v^2}{r}PE = mgh
 KE_i + PE_i = KE_f + PE_f
MomentumTorque and Rotations
p = m v\tau = r \cdot F \cdot \sin(\theta)
J = \Delta pI = \sum mr^2
p_i = p_fL = I \cdot \omega
Simple Harmonic Motion
F = -k x
T = 2\pi \sqrt{\frac{l}{g}}
T = 2\pi \sqrt{\frac{m}{k}}
ConstantDescription
gAcceleration due to gravity, typically 9.8 , \text{m/s}^2 on Earth’s surface
GUniversal Gravitational Constant, 6.674 \times 10^{-11} , \text{N} \cdot \text{m}^2/\text{kg}^2
\mu_k and \mu_sCoefficients of kinetic (\mu_k) and static (\mu_s) friction, dimensionless. Static friction (\mu_s) is usually greater than kinetic friction (\mu_k) as it resists the start of motion.
kSpring constant, in \text{N/m}
M_E = 5.972 \times 10^{24} , \text{kg} Mass of the Earth
M_M = 7.348 \times 10^{22} , \text{kg} Mass of the Moon
M_M = 1.989 \times 10^{30} , \text{kg} Mass of the Sun
VariableSI Unit
s (Displacement)\text{meters (m)}
v (Velocity)\text{meters per second (m/s)}
a (Acceleration)\text{meters per second squared (m/s}^2\text{)}
t (Time)\text{seconds (s)}
m (Mass)\text{kilograms (kg)}
VariableDerived SI Unit
F (Force)\text{newtons (N)}
E, PE, KE (Energy, Potential Energy, Kinetic Energy)\text{joules (J)}
P (Power)\text{watts (W)}
p (Momentum)\text{kilogram meters per second (kgm/s)}
\omega (Angular Velocity)\text{radians per second (rad/s)}
\tau (Torque)\text{newton meters (Nm)}
I (Moment of Inertia)\text{kilogram meter squared (kgm}^2\text{)}
f (Frequency)\text{hertz (Hz)}

General Metric Conversion Chart

Example of using unit analysis: Convert 5 kilometers to millimeters. 

  1. Start with the given measurement: \text{5 km}

  2. Use the conversion factors for kilometers to meters and meters to millimeters: \text{5 km} \times \frac{10^3 \, \text{m}}{1 \, \text{km}} \times \frac{10^3 \, \text{mm}}{1 \, \text{m}}

  3. Perform the multiplication: \text{5 km} \times \frac{10^3 \, \text{m}}{1 \, \text{km}} \times \frac{10^3 \, \text{mm}}{1 \, \text{m}} = 5 \times 10^3 \times 10^3 \, \text{mm}

  4. Simplify to get the final answer: \boxed{5 \times 10^6 \, \text{mm}}

Prefix

Symbol

Power of Ten

Equivalent

Pico-

p

10^{-12}

Nano-

n

10^{-9}

Micro-

µ

10^{-6}

Milli-

m

10^{-3}

Centi-

c

10^{-2}

Deci-

d

10^{-1}

(Base unit)

10^{0}

Deca- or Deka-

da

10^{1}

Hecto-

h

10^{2}

Kilo-

k

10^{3}

Mega-

M

10^{6}

Giga-

G

10^{9}

Tera-

T

10^{12}

  1. Some answers may be slightly off by 1% depending on rounding, etc.
  2. Answers will use different values of gravity. Some answers use 9.81 m/s2, and other 10 m/s2 for calculations.
  3. Variables are sometimes written differently from class to class. For example, sometime initial velocity v_i is written as u ; sometimes \Delta x is written as s .
  4. Bookmark questions that you can’t solve so you can come back to them later. 
  5. Always get help if you can’t figure out a problem. The sooner you can get it cleared up the better chances of you not getting it wrong on a test!

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