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The following questions ask you to solve problems involving Newton’s laws and forces
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Work out each problem and post an image of your work for each question along with a brief description of how you solved the problem.
Your scanned work should include a free body diagram showing all forces acting on the object(s), as well as a step-by-step solution to the problem.
Question 1 A 2 kg book resting on a flat table requires an applied force of 4 N to make it move. Draw a free body diagram illustrating this situation and find the coefficient of static friction between the book and the table.
Question 2 A 30 kg crate is pulled across a flat floor with 80 N of force. The coefficient of kinetic friction between the crate and the floor is 0.15. Draw a free body diagram illustrating this situation and find the acceleration of the crate.
Question 3 An applied force of 100 N causes a 20 kg crate to accelerate across a level floor at 2 m/s2. Draw a free body diagram illustrating this situation and find the coefficient of kinetic friction between the crate and the floor.
Question 4 60 N of force is applied to a 10 kg crate initially at rest on a level floor. The coefficient of friction between the crate and the floor is 0.4. Draw a free body diagram illustrating this situation and find the distance traveled and the velocity of the crate after 3 seconds.
Question 5 Sue and Bill are standing on a frictionless surface of ice. Sue, whose mass is 60 kg, pushes Bill, mass 100 kg, with 300 N of force. Draw a free body diagram illustrating this situation and find the acceleration of both Sue and Bill.
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Week 2 Overview |
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Last week, we studied the relationship between acceleration, velocity, displacement, and time. Acceleration in an object is caused by the force acting on it. This week, we’ll study the relationship between force and acceleration. Central to this study are the laws of motion that Isaac Newton discovered in the 17th century. You must have observed in daily life that when you apply brakes to a car, it takes some time before the car stops completely. The speed with which a train moves depends on the amount of force applied by the engine. A ball thrown at a wall bounces back. Newton’s laws help you understand the motion of day-to-day objects and explain all this phenomena. These laws can also help you create realistic graphic animations! |
Have you ever walked on slippery surfaces? If so, you would have realized how difficult it is to walk on them. Slippery surfaces have less friction, which makes it difficult to walk. In fact, surface transportation would be impossible without friction. This week, we take a closer look at this important force. We will use Newton’s laws to analyze problems involving friction.
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Newton’s First Law |
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What are Forces? Forces are the result of the interaction between bodies. In simple words, a force is the push or pull acting on an object. For example, you exert a force on a rope to pull an object, and the rope pulls the object. Here, we need a transition between the definition of forces and Newton’s Laws. We also need a couple of examples of how to draw a force diagram. The Law of Inertia Newton’s first law of motion explains the relation between the force applied on an object and its motion. The law states that: An object continues to remain in a state of rest or of uniform motion in a straight line unless compelled by an external force to act otherwise. This means that an object prefers to remain in a state of rest or uniform motion; in order to change the state it’s in you need to apply force to it. Further, an object will always resist the force applied to it. The property of an object to resist an external force is called inertia, and for this reason, Newton’s first law is called the law of inertia. |
If you slide an object on a smooth floor with a given speed, the distance it moves depends upon the friction between the object and the floor. The smoother the floor, the greater the distance traveled by the object. The object eventually stops because of the external force of friction.
A force is required to change the velocity of a body. To understand this statement first recall from your study of kinematics that velocity is a vector with a magnitude (speed) and a direction. In the absence of a force, both speed and direction are constant. When a force acts on an object, it changes the speed, direction, or both of the objects.
There is no basic difference between an object at rest and an object in uniform motion; rest and uniform motion are relative terms. An object at rest with respect to one observer may have a uniform velocity with respect to another observer.
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Newton’s Second and Third Laws (1 of 2) |
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Newton’s Second Law Newton second law states that: The acceleration of an object is proportional to the applied force and takes place in the direction of the impressed force. An object may experience a number of forces at any instant; one of them is the gravitational force, which always acts on an object in addition to other forces. The vector sum of all the forces acting on an object at any instant is known as the net force. According to Newton’s second law, acceleration is proportional to the net force acting on an object and takes place in the direction of the net force. Therefore, if the force on an object is doubled, the acceleration will also be doubled. The relation between the force and acceleration of an object depends on the mass of the object; when the mass increases, the same force produces less acceleration. Mathematically, Newton’s second law is expressed as: F = ma |
Newton’s second law gives us a quantitative measure of the acceleration of an object when a force acts on it. While calculating the acceleration caused by a force, remember that the direction of acceleration is always in the direction of the force and its magnitude depends on the magnitude of the force and the mass of the object.
Because force and acceleration are vectors, Newton’s second law can be applied in any direction you want. The sum of the components of all forces in a given direction equals the product of the mass and the acceleration component in that direction.
Newton’s second law is also used to define the unit of force, Newton (N), as the force required to accelerate an object with a mass 1 kg by 1 m/s2. Thus, 1 N = 1 kgm/s2.
Inertial Reference Frames
An important consideration while applying Newton’s first and second laws is that these laws can be applied only by observers who are themselves not accelerating. For example, a person sitting in an accelerating car or riding a roller coaster cannot apply Newton’s first or second law. The person should be located in another frame of reference where he is not experiencing the force being analyzed. Frames of reference where Newton’s laws are applicable are called inertial reference frames.
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Newton’s Second and Third Laws (2 of 2) |
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Newton’s Third Law Now let’s study about Newton’s third law. It states that: To every action (force) there is an equal and opposite reaction (force). |
According to this law, all forces occur in pairs, called action-reaction pairs. When one object exerts a force on another object, the second object exerts an equal and opposite force on the first object.
It is important to note that the action and reaction forces act on different objects. For example, if you push a car (action), the car in turn pushes you back (reaction). Because the action and reaction forces are not acting on the same objects, they don’t cancel each other. If action and reaction were to act on the same object, then all the forces on an object would be in exact balance, and the object would never accelerate.
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Application of Newton’s Laws (1 of 3) |
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Newton’s laws of motion can be used to solve a wide variety of problems that involve force and motion. Let’s apply Newton’s laws to find the acceleration produced by a force in a wheelbarrow. |
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Application of Newton’s Laws (2 of 3) |
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Imagine a statue resting on a table. It is acted upon by various objects, and in turn, it reacts on those objects. Let’s use Newton’s laws to analyze the forces acting on the statue. What are the forces acting on the statue? One of the forces is the pull that the Earth exerts on the statue called the weight of the statue. If the table suddenly disappears, the statue will fall down with an acceleration of 9.8 m/s2 until it hits the floor and perhaps shatters to pieces. However, the table prevents this from happening. The table must be exerting an upward force on the statue equal to the weight of the statue, given by Newton’s second law, F = mg applied in the vertical direction. Because the statue is not moving either up or down, it does not have acceleration either upward or downward. Therefore, there is no net force on the statue. The weight of the statue is acting downward, so the table must be exerting an equal force upward. Is the force exerted by the table on the statue the reaction to the weight of the statue? No, it is not. Both these forces act on the statue and cannot be an action-reaction pair. Recall that the weight of the statue is the force with which the Earth attracts the statue. The reaction force is the force with which the statue attracts the Earth. Then what about the reaction force to the force exerted by the table? Because the statue and the table are in contact, the table pushes up on the statue, and the statue presses down on the table with an equal force. We have already shown that the upward force exerted by the table is equal in magnitude to the weight of the statue. Therefore, the statue presses down on the table with a force equal to the weight of the statue. This force is called the normal force, FN, as it is always perpendicular to the surface, or normal to the surface. |
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Application of Newton’s Laws (3 of 3) |
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Often when analyzing how forces act on an object, it is helpful to draw a free body diagram. A free body diagram is a drawing showing all of the forces acting on the object, as well as the net force if applicable. For the previous example of a statue resting on a table, we would draw the following free body diagram: |
Friction
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Friction forces arise when objects rub against each other. Friction acts parallel to the surface and opposes motion. Even though friction opposes motion, it doesn’t always play a negative role. Without friction, all forms of surface transport including walking and running will be impossible. Experiments show that there are two types of friction forces: · Static friction · Kinetic friction Let’s look at each one of them. Static Friction It is a common experience that if a heavy object such as a crate is pulled or pushed, the object does not begin to move unless the force applied reaches a critical value. Below this critical value, a static friction force prevents motion. The static friction adjusts itself so that it is equal to the applied force up to a limit. If the applied force exceeds this limit, the static friction does not increase any further and the body starts to slide. The limiting value of static friction is found from experiments to be directly proportional to the force with which the object is pressing the floor, in other words, the normal force. For a horizontal surface, the normal force, FN, is equal to the weight, FG, of the object. The maximum static friction can be expressed as: FFric = μSFN The constant μ does not have any units because it is the ratio of two forces. μ is called the coefficient of friction. It represents how the force of friction depends upon the “roughness” of the surfaces in contact. The coefficient of friction is different for different combinations of surfaces. Here, we’ve labeled it μS to indicate that it is the coefficient of static friction. Let’s solve an example based on the above equation. |
Drag
When you swim, you feel the resistance of the water to your motion. Friction forces are also present when a body moves in a fluid. This force is called the drag force. Of particular interest is the motion of bodies in air. Air too is a fluid and offers resistance to motion. When blunt objects such as a ball move through the air, the drag force is found to be proportional to the square of its speed. This means that the drag increases by four times if the speed is doubled. As a result, high-speed vehicles are given a sleek shape to reduce the cross-section area A so that drag is reduced.
Terminal Velocity
Why does a raindrop have such a low speed of about 7 m/s considering that it is falling from such a height? If the drop is assumed to fall from a height of 500 m and accelerates all the way down, it would have a speed of 225 mi/h. It would be dangerous to go out in the rain! The answer is that drag forces limit the speed of falling drops.
As the drops fall, they initially accelerate due to their weight, but as the velocity increases, drag also increases as the square of the velocity. When the drop reaches a velocity of 7 m/s, the drag force is equal to the weight of the drop. From Newton’s second law (or first law) there is no net force on the drop and the drop continues to move at 7 m/s thereafter. This constant velocity is called the terminal velocity of the drop, and it is different for different objects. A skydiver in a free fall has a terminal velocity of about 60 m/s. The skydiver can vary the velocity within limits by varying the cross-sectional area he offers perpendicular to the direction of motion.
A parachute also works on the principle of terminal velocity. By offering a large cross-sectional area, the parachute quickly attains a terminal velocity of a few meters per second and safely brings the parachutist down to the ground.
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Week 2 Summary |
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This week, you studied about Newton’s laws of motion. Newton’s first law is about inertia, which resists the force applied on an object if the direction of the force is opposite to the direction of motion of the object. Newton’s second law, F = ma, provides a relationship between force, mass, and acceleration of an object. Newton’s third law states that all forces act in pairs, called action-reaction pairs. Use the knowledge gained during the week to understand and solve problems related to force, mass, acceleration, and friction in real life. |
