Newton's Laws of Motion

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Questions and Answers

Which statement accurately describes the forces acting on a body moving with constant speed in a straight line?

  • The net force acting on the body is equivalent to zero. (correct)
  • A single constant force opposes the body's direction of motion.
  • A constant net force acts on the body in its direction of motion.
  • A single constant force propels the body in its direction of motion.

An object with mass m is traveling at an initial velocity of 25.0 m/s and comes to rest over a distance of 62.5 m due to a constant force of 15.0 N. What is the mass of the object?

  • 1.50 kg (correct)
  • 3.00 kg
  • 6.00 kg
  • 3.75 kg

An object moves to the right at a constant speed. What statement is correct regarding the forces acting on the object?

  • No forces are acting on the object.
  • The net force acting on the object is directed to the right.
  • The net force acting on the object is zero. (correct)
  • More forces push the object to the right than to the left.

A force F causes an object of mass m to accelerate at a rate a. If a force of 3_F_ is applied to a second object, resulting in an acceleration of 8_a_, what is the mass of the second object?

<p>(3/8)<em>m</em> (C)</p> Signup and view all the answers

A 2.0 kg ball is subjected to two forces: $\vec{F_1} = 3.0N \hat{i} + 4.0N \hat{j}$ and $\vec{F_2} = -5.0N \hat{i} + 6.0N \hat{j}$. Determine the magnitude of the ball's acceleration.

<p>5.1 m/s² (A)</p> Signup and view all the answers

Four diagrams depict a force F applied to a block of mass m. Assuming no friction, which scenario results in the greatest acceleration of the block in the horizontal direction?

<p>Diagram (3) (B)</p> Signup and view all the answers

A block slides down a frictionless inclined plane. Which of the free-body diagrams correctly represents the forces acting on the block?

<p>2 (C)</p> Signup and view all the answers

Under what condition would a person in an elevator experience an apparent weight greater than their actual one?

<p>The elevator is moving downward with decreasing speed. (B)</p> Signup and view all the answers

Two metal blocks with different masses are released simultaneously on the same frictionless incline. Which statement accurately describes their motion?

<p>They experience equal accelerations. (B)</p> Signup and view all the answers

A 6-kg block on a smooth table is connected by a massless cord over a frictionless pulley to a freely hanging 2-kg mass. What is the acceleration of the two-block system?

<p>one-fourth of g (D)</p> Signup and view all the answers

A force of F = 90 N is exerted at an angle of 25 degrees to the horizontal on mass m₁, which is connected to mass m₂ = 10 kg. Both masses accelerate to the right at 3 m/s² along a frictionless surface. What is the value of mass m₁?

<p>17 kg (B)</p> Signup and view all the answers

A 100-kg block is pushed up a 30° incline that is 10 m long. The coefficient of friction between the block and the incline is 0.1. Approximately what constant force, parallel to the incline, is required to move the block from rest at the bottom to the top in 3 s?

<p>0.58 kN (B)</p> Signup and view all the answers

Four identical blocks are moving on a surface with a coefficient of kinetic friction µk. A vector indicates the velocity of each block. For which block is the force of kinetic friction the greatest?

<p>The force of friction is the same for all blocks. (A)</p> Signup and view all the answers

A block of wood is pulled horizontally across a rough surface at a constant velocity with a force of 20 N. If the coefficient of kinetic friction between the surfaces is 0.3, what is the magnitude of the friction force?

<p>20 N (B)</p> Signup and view all the answers

A block of mass m is pulled across a rough surface at a constant velocity. The pulling force is T and the angle between the rope and the surface is $\theta$. What is the magnitude of the frictional force?

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A horizontal force F is used to push an object of mass m up an inclined plane at an angle $\theta$ with the horizontal. Determine the normal reaction force exerted by the plane on the mass.

<p>$mg \cos\theta + F \sin\theta$ (A)</p> Signup and view all the answers

A car travels around a curve with radius R at speed V and experiences a centripetal acceleration ac. What is the car's centripetal acceleration if it travels around a curve with radius 3_R_ at a speed of 2_V_?

<p>(4/3)<em>ac</em> (A)</p> Signup and view all the answers

A ball on the end of a string travels counterclockwise in a circular path. Assume air resistance is negligible. Which free-body diagram best represents the net force acting on the ball?

<p>4 (D)</p> Signup and view all the answers

Flashcards

Newton's First Law Implication

A body moving at a constant speed in a straight line experiences zero net force.

Object Moving at Constant Speed

With constant speed there is no net force acting on the object.

Mass and Acceleration Relationship

The mass of the second object is (3/8)m

Net Force and Acceleration

The magnitude of acceleration is 3.9 m/s².

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Free-Body Diagram

The correct free-body diagram is (1).

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Apparent Weight > Actual Weight

The elevator moves upward with decreasing speed.

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Blocks on Frictionless Inclines

They have equal accelerations.

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Connected Masses and Acceleration

The acceleration of the two-block system is one-fourth of g.

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Force at an Angle

The mass m1 is 17 kg.

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Force on an Incline with Friction

The constant force parallel to the incline that is required to move the block from rest at the bottom of the incline to the top in 3 s is approximately 0.58 kN

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Kinetic Friction on Moving Blocks

The force of friction is the same for all blocks.

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Force and Friction at Constant Velocity

The force of friction is 20 N

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Friction with an Applied Force

The magnitude of the frictional force is μk(mg – T sin θ)

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Normal Reaction Force on Inclined Plane

mg cos θ + F cos θ

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Centripetal Acceleration

(4/3)ac

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Net Force in Circular Motion

The free-body diagram that best represents the net force acting on the ball is 3.

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Study Notes

Newton's Law

  • For a body moving at a constant speed in a straight line, the net force acting on it is zero.
  • A mass 'm' traveling at an initial speed v0 = 25.0 m/s comes to rest over a distance of 62.5 m with a 15.0 N force; its mass is 3.75 kg.
  • When an object moves to the right at constant speed, there's no net force acting on it.
  • Force F causes acceleration 'a' on mass 'm'; force 3F causing acceleration 8a on a second object means the second object's mass is (3/8)m.
  • A 2.0 kg ball acted on by forces F1 = 3.0N i + 4.0N j and F2 = -5.0N i + 6.0N j experiences an acceleration of 5.1 m/s².
  • The largest acceleration on a block in the horizontal direction occurs when the force F is applied directly horizontally, without any opposing or compounding forces.
  • Illustrating a block sliding down a frictionless inclined plane, the free-body diagram should show gravity acting downwards, a normal force perpendicular to the plane, and no friction.
  • Apparent weight exceeding actual weight in an elevator indicates it is moving downward with decreasing speed.
  • Two metal blocks freely sliding down a frictionless incline have equal accelerations, irrespective of mass differences.
  • For a 6-kg block on a smooth table connected to a 2-kg hanging mass over a pulley, the system's acceleration is one-fourth of g (gravitational acceleration).
  • With a 90 N force at 25 degrees to the horizontal exerted on mass m1, and both m1 and m2 accelerating at 3 m/s², where m2 = 10 kg, the mass m1 is calculated to be 17 kg.

Newton's Law (Friction & Circular Motion)

  • A 100-kg block pushed up a 30° incline (10 m long) with a friction coefficient of 0.1 requires approximately 0.58 kN of force to move from the bottom to the top in 3 seconds.
  • Four identical blocks moving across a surface with kinetic friction µk experience the same friction force, regardless of their velocity vectors.
  • A wooden block pulled horizontally across a rough surface at constant velocity with 20 N force, where the kinetic friction coefficient is 0.3, experiences a friction force of 20 N.
  • For a block of mass 'm' pulled across a rough surface at a constant velocity with force T at an angle, the friction magnitude is µk(mg – T sin ).
  • With a horizontal force F pushing a mass 'm' up an inclined plane (angle ), the normal reaction force is mg cos + F sin .
  • If a car has centripetal acceleration 'ac' when turning at speed V around radius R, then at 2V around radius 3R, its acceleration becomes (4/3)ac.
  • In a top view of a ball traveling counterclockwise in a circle at the end of a string, and negligible air resistance, the force diagram depicting the net force has the force pointing towards the center of the circle.

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