Grade 9: Free-Body Diagrams and Combining Forces

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Questions and Answers

In which scenario is the net force acting on an object equal to zero?

  • A car accelerating from rest.
  • A skydiver accelerating downwards.
  • A ball rolling down a ramp.
  • A book resting on a table. (correct)

Which of the following best describes a free-body diagram?

  • A diagram showing all forces acting on a system. (correct)
  • A diagram showing the internal forces within an object.
  • A diagram showing the motion of an object over time.
  • A diagram showing only the gravitational force acting on an object.

How does the length of an arrow in a free-body diagram relate to the force it represents?

  • The length is inversely proportional to the magnitude of the force.
  • The length is arbitrary and does not represent any physical quantity.
  • The length is proportional to the magnitude of the force. (correct)
  • The length indicates the direction of the force, not the magnitude.

What is the relationship between action and reaction forces according to Newton's Third Law?

<p>Action and reaction forces act on different objects and are equal in magnitude. (A)</p> Signup and view all the answers

When analyzing forces, how is Earth typically treated when considering a small object interacting with it?

<p>Earth is often treated as part of the external world due to its large mass. (A)</p> Signup and view all the answers

What is the proper unit to measure weight?

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

What term describes the support force exerted on an object, such as a scale exerting a force on a person?

<p>Apparent weight (D)</p> Signup and view all the answers

How does the apparent weight of an object compare to its real weight when the object is in an elevator accelerating upwards?

<p>The apparent weight is greater than the real weight. (D)</p> Signup and view all the answers

You are holding a 1-kilogram mass suspended from a spring scale inside an elevator. If the scale reads 9.3 N, what can be inferred about the elevator's motion?

<p>The elevator is accelerating downwards. (D)</p> Signup and view all the answers

Under what condition are the apparent and real weights of an object the same?

<p>When the object is moving at a constant velocity. (A)</p> Signup and view all the answers

An object in equilibrium in a coordinate system has vectors acting on it. For angles less than $90°$ and greater than $270°$, which of the following is correct?

<p>The x-component is positive. (D)</p> Signup and view all the answers

Which statement accurately describes the relationship between a vector and its components?

<p>A vector can be equal in length to one of its components if it lies along that axis. (B)</p> Signup and view all the answers

If you walk 8.0 km north and then walk east until your displacement from home is 10.0 km, approximately how far east did you walk?

<p>6 km (A)</p> Signup and view all the answers

In a tug-of-war, one team ties their end of the rope to a tree while the other team pulls with a 500 N force. Assuming the rope is in equilibrium, what is the tension in the rope?

<p>500 N (A)</p> Signup and view all the answers

Two horizontal forces are exerted on a large crate. One force is 317 N to the right and the other is 173 N to the left. If the crate is initially at rest and, after five seconds, its velocity to the right is 6.5 m/s, what is the crate's mass?

<p>111 kg (C)</p> Signup and view all the answers

Flashcards

Free-Body Diagram

A physical representation showing forces acting on a system. Drawn separately, uses particle model, shows force vectors.

Net Force

The vector sum of all forces acting on an object.

Apparent Weight

The support force exerted on an object.

Weight

The gravitational force experienced by an object.

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Gravitational Field

The name given to the gravitational force exerted by Earth on an object.

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Newton's Third Law

The force of A on B is equal in magnitude and opposite in direction of the force of B on A

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Interaction Pair

Forces that are in opposite directions, have equal magnitudes, and act on different objects.

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Study Notes

  • Grade 9 - Term 2 End of Term 2 Exam Coverage 2024-2025 Part 1

Free-Body Diagrams

  • A free-body diagram is a physical representation showing the forces acting on a system.
  • Free-body diagrams are drawn separately from the sketch of the problem situation.
  • The object is represented as a dot.
  • Forces are represented with arrows pointing in the direction of the force, drawn away from the dot.
  • The length of arrows is proportional to the size of the force.
  • Forces are labeled with the symbol F and a subscript label to identify the agent and the object.
  • A direction must be chosen to be positive and is indicated in the diagram.

Combining Forces

  • Forces in the same direction can be summed to form a resulting force.
  • Forces in opposite directions are combined by taking the difference between them.
  • The vector sum of all the forces on an object is the net force.
  • If the net force is zero, then the forces are balanced, and there is no acceleration.
  • If the forces are unbalanced, there will be acceleration.

Skydiver and Softball Examples

  • For a skydiver falling at a constant velocity, the force of air resistence on the diver equals the force of Earth's mass on the diver, indicated by Fnet = 0.
  • When holding a softball, the hand on ball contact force equals the Earth's mass on ball gravity force.
  • After a softball leaves a hand it will rise and slow down.
  • After the softball reaches maximum height it will falls down and speed up.

Connecting Interaction Pairs and Newton's Third Law

  • Forces always come in pairs.
  • An interaction pair is a set of two forces that are in opposing directions, have equivalent magnitude and act on different objects
  • Newton's Third Law states that all forces come in pairs.
  • The two forces in a pair act on different objects, are equal in strength, and are opposite in direction.
  • With forces like Earth's mass on a ball, and a ball on Earth's mass, the Earth's acceleration is negligibly small due to the large mass of the Earth compared to small objects.
  • If you lift a bowling all your hand exerts a force on the ball, and the Earth exerts a gravitational force on the ball. and the ball exerts a force on your hand and a gravitational force on Earth.
  • A suitcase on a cart has a gravitational force of the Earth on the suitcase, and the surface of the cart exerts a force on the suitcase. The suitcase force on the cart, and the suitcase on the Earth.
  • When a ball is tossed in the air, after it loses contact with a hand, the Earth's mass is the acting force on the ball.

Apparent Weight

  • Apparent weight is the support force exerted on an object.
  • Weightlessness means there are no contact forces supporting the object, so apparent weight is zero.
  • When traveling at a constant velocity the apparent weight and real weight are equal.
  • Apparent weight is less than real weight when the velocity is slowing while rising, or speeding up while descending.
  • Apparent weight is greater than real weight when the velocity is speeding up while rising, or slowing while descending.
  • When a scale is read at a different weight than the object's weight, there is an acceleration of the elevator
  • At a constant velocity, the scale's weight will read the objects mass times gravity.

Formula for Weight

  • Weight is defined as the gravitational force on an object, given by F = mg , where m is the object's mass and g is the gravitational field (9.8 N/kg on Earth).

Combining Forces

  • To solve for the force on a crate that has one force of 317N to the right, and 173 N to the left the equation used is Fnet = 317 N -173 N

Solving Vector Problems

  • To solve a vector problem the components must be calculated.
  • To solve for displacement you must first calculate the components, and then use the components in the Pythagorean Theorem.
  • A vector can be shorter, but never longer than its components.

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