Atwood's Machine: Gravity & Motion

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Questions and Answers

What factor determines the net force acting on the system of masses in an Atwood's Machine?

  • The product of the weights of the two hanging masses
  • The difference in weight between the two hanging masses (correct)
  • The sum of the weights of the two hanging masses
  • The average weight of the two hanging masses

In an Atwood's machine with unequal masses, the heavier mass accelerates upward, while the lighter mass accelerates downward.

False (B)

What is the standard value of acceleration due to gravity on Earth, expressed in meters per second squared?

9.81 m/s^2

In free fall, in the absence of air resistance, the speed of a ball thrown from a cliff increases by approximately ______ m/s every second.

<p>9.8</p> Signup and view all the answers

Match the following scenarios with the appropriate type of motion under gravity:

<p>Object thrown upwards = Free fall Object released from rest = Free fall Object moving downwards = Free fall</p> Signup and view all the answers

According to Newton's Second Law, what is the relationship between the net force (\Sigma F), mass (m), and acceleration (a) of an object?

<p>\Sigma F = ma (A)</p> Signup and view all the answers

In an Atwood's Machine, the tension in the string is always equal to the weight of the heavier mass.

<p>False (B)</p> Signup and view all the answers

In an Atwood's Machine, what is assumed about the pulley and string for simplified calculations?

<p>massless pulley and non-stretchable string</p> Signup and view all the answers

In a sample problem involving an Atwood's Machine, if mass 1 is 10 kg and mass 2 is 5 kg, the acceleration is assumed to be ______ if it's counterclockwise

<p>positive</p> Signup and view all the answers

Match the following components of force analysis for an Atwood's Machine:

<p>F_net = Net force acting on a mass F_grav = Gravitational force acting on a mass F_tens = Tension in the string</p> Signup and view all the answers

In the free body diagram of mass m_1 in an Atwood's machine (assuming m_1 > m_2), which of the following is correct?

<p>The tension (T) points upwards, and the weight (W₁) points downwards. (C)</p> Signup and view all the answers

In an Atwood's Machine, if the two masses are equal, the acceleration of the system is non-zero.

<p>False (B)</p> Signup and view all the answers

In an Atwood's Machine, how should the masses be related such that there is no acceleration?

<p>m1 = m2</p> Signup and view all the answers

If the acceleration (a) of a system in Atwood's machine is negative, it indicates that m_1 is ______ than m_2.

<p>less</p> Signup and view all the answers

Relate the mathematical expressions with the physical terms

<p>T = g(m_1)/(m_1 + m_2) = Incorrect expression for tension T = 2g(m_1 m_2)/(m_1 + m_2) = Tension in the string T = g(m_1 m_2)/(m_1 - m_2) = Incorrect expression for tension</p> Signup and view all the answers

In lab measurements of an Atwood machine, what does the slope of the speed versus time graph represent?

<p>The acceleration of the system. (C)</p> Signup and view all the answers

Inclined planes are used to move loads only from high to low places, not the other way around.

<p>False (B)</p> Signup and view all the answers

Name the forces acting on a package moving down an incline?

<p>normal force</p> Signup and view all the answers

The normal force on an object lying on an inclined plane with no friction is ______ to the plane's surface.

<p>perpendicular</p> Signup and view all the answers

Match the force components with their corresponding description on an inclined plane with no friction

<p>F_{\parallel} = Net force and parallel to the plane F_{\perp} = Component perpendicular to the inclined plane F_{grav} = Force of gravity</p> Signup and view all the answers

What is the net acceleration of an object on an inclined plane (angle θ) with friction (coefficient μ)?

<p>a = g(sin θ - μ cos θ) (A)</p> Signup and view all the answers

The force that must be applied by the brakes to keep a car from moving on an inclined hill is equal to the car's normal force.

<p>False (B)</p> Signup and view all the answers

If the mass of car is m, hill inclination is θ, what is the expression for force applied by brake to stop it from moving?

<p>mg sin(θ)</p> Signup and view all the answers

The gravitational force on a 50 kg box on a frictionless inclined plane is directly proportional to its ______.

<p>mass</p> Signup and view all the answers

A mass m is placed on a frictionless inclined plane. Match the forces to its expression

<p>Normal force = mg cos θ Component of weight that accelerates the mass = mg sin θ Gravitational Force = mg</p> Signup and view all the answers

A car is parked on a hill with a 20° slope. If the car's mass is 1000 kg, what is the component of the gravitational force acting parallel to the hill's surface?

<p>Approximately 3,352 N (B)</p> Signup and view all the answers

An inclined lane dynamics track can be used to determine acceleration of different masses

<p>True (A)</p> Signup and view all the answers

What equipment can be used to find the acceleration of the cart running down the track in the experiments?

<p>inclined dynamics track</p> Signup and view all the answers

In the cart experiment, for each angle, you will measure the ______ at 2 different points on the track and from there determine the acceleration.

<p>velocity</p> Signup and view all the answers

Match each variable to the correct physics quantity in the following equation for finding acceleration: v_2^2 = v_1^2 - 2 a Δx

<p>v_1 = initial velocity v_2 = final velocity a = acceleration Δx = distance</p> Signup and view all the answers

What property does inclined plane change?

<p>It allows for easier lift (A)</p> Signup and view all the answers

Acceleration is variable for the object moving on the inclined plane.

<p>False (B)</p> Signup and view all the answers

If an object mass is m on an inclined plane which one is affected by gravity? All mass or some part of it?

<p>some part</p> Signup and view all the answers

On an inclined plane mass (m) object has force equations as F_N = F_g and mass is constant motion, on the other hand if it is moving then force equation becomes F_{net} = ma = ______

<p>mg sin θ</p> Signup and view all the answers

Match each variable with their value on inclined hill with 20° slope, car Weight 1,000 kg

<p>F_N = 9,209N mg = 9,800N F_{brakes} = 3,351.8N</p> Signup and view all the answers

The acceleration due to gravity is also called

<p>free fall (A)</p> Signup and view all the answers

Objects thrown upward or downward and those released from rest are all examples of free fall.

<p>True (A)</p> Signup and view all the answers

The standard equations of a uniformly accelerated body are applicable for _______

<p>free fall</p> Signup and view all the answers

Objects in free fall experience constant _______

<p>acceleration</p> Signup and view all the answers

Match the following concepts:

<p>Elevators = Atwood machine Garage doors = Atwood machine wells = Atwood machine</p> Signup and view all the answers

Flashcards

Atwood's Machine

A machine consisting of two objects of unequal mass suspended vertically by a string over a light frictionless pulley.

Acceleration due to Gravity

The acceleration experienced by an object due to the gravitational force exerted by a massive body.

g = 9.81 m/s²

The standard value of acceleration due to gravity on Earth.

Free fall

An object moving only under the influence of gravity.

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Newton's Second Law

A relationship where the force equals mass times acceleration.

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Atwood's Machine: Net Force

The difference in weight between two hanging masses, determines the net force acting on each mass.

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Motion on an Inclined Plane

Motion of an object along a surface tilted at an angle relative to the horizontal.

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Fnet

The net force in the Parallel direction to the inclined plane

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Normal Force

A force the surface exerts on an object, perpendicular to the plane's surface.

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Weight Component (Parallel)

Component of the weight force acting parallel to the inclined plane.

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Acceleration with Friction

The acceleration when friction affects an object on an inclined plane.

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Force of Friction

The force that opposes motion, depends on normal force and coefficient of friction.

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gravatational force?

This is equal to the standard value of acceleration due to gravity on Earth multiplied by a mass, g* mass.

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Study Notes

Atwood's Machine

  • Atwood's Machine features two objects with different masses
  • The objects are hung vertically using a string over a light frictionless pulley
  • The system accelerates if one mass is greater
  • Elevators, garage doors, and wells are real world applications

Net Force

  • An Atwood's Machine net force depends on the weight difference of the hanging masses
  • Gravity causes acceleration, with the heavier mass accelerating downward and the lighter mass upward

Acceleration due to Gravity

  • Acceleration due to gravity is the acceleration an object experiences from a massive body's gravitational pull such as Earth
  • The standard value of gravity on Earth is 9.81 m/s²

Free Fall

  • In the absence of air resistance, objects in free fall near Earth accelerate at 9.81 meters per second squared
  • If throwing a ball off a cliff, its speed increases by 9.8 m/s every second unless there is air resistance
  • Gravity causes the change in speed
  • Free fall doesn't only mean moving downwards, but objects release from rest or thrown upward/downward too
  • Uniformly accelerated body equations apply to free fall

Atwood's Machine Equations

  • This assumes a pulley with no mass, a non-stretchable string, and no friction
  • T - m₁g = Fnet (on mass m₁) = m₁a
  • m₂g - T = Fnet (on mass m₂) = m₂a
  • The acceleration can be expressed as a = ((M₂ - M₁) / (M₂ + M₁)) * g

Sample Problem

  • In a sample problem, positive acceleration is assumed to be counterclockwise
  • Acceleration of the two masses remains the same
  • The value of a = (m_1 - m_2) / (m_1 + m_2) * g
  • If mass 1 is 10.0kg and mass 2 is 5.0 kg then a = 3.27m/s²

Sample Problem Force Analysis

  • Net force equals mass times acceleration and is also the gravitational force less tension
  • Consider the 10.0 kg weight with a gravitational force of 98.0 N
  • Net force equals 32.7 N, with the tension force calculated as 65.3 N

Motion Experiment

  • Experimentally, measure masses' motion on an Atwood Machine
  • Capstone is used to compute speed
  • Acceleration is the slope of the speed versus time on a graph

Motion on an Inclined Plane

  • This is the movement of an object on a surface tilted at an angle, θ, relative to the horizontal
  • Inclined planes are work-saving devices used to move loads between different heights

Forces on Inclined Plane

  • Gravity acts directly downwards
  • The normal force is surface force and is perpendicular to surface of the plane
  • If there is no friction, these two forces are normally all that are acting on the object

Friction

  • With no friction:
  • Fn = Fg
  • F_N = mg cos θ
  • Fnet = ma = mg sin θ
  • If friction is added ( f = μN, f = μmg cos θ)
  • Net acceleration becomes: a = g(sin θ – μ cos θ)
  • mu = the coefficient of friction.

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