In the example above, we want the top of the fraction to be the same as the bottom. The slope of the tangent line example 2. What is the velocity at the point shown by a dot on the graph. Compare the accelerations of the rock and the bullet while they are in the air on the way down.

What force is newton's third law partner of the earth's gravitational force in the book. The forces are not of the same type because the upward force of the table in the book is not gravitational.

## Analysis of Forces

The dimples in the golf ball change the flow pattern of the air around it, reducing friction in a counter-intuitive way. It also depends on the shape of the object. Therefore, a fighter jet is more streamlined than a Model T. For objects of the same shape but different sizes, fluid friction generally increases with the cross-sectional area of the object. is one of the main reasons that an SUV gets worse highway mileage than a compact car.

Here I have used the word "floating" force as an example of a sensible coined term for a type of force not classified in the tree in the previous section. Notice how the force pairs are all structured as “A's force on B, B's force on A”: ropes on barge and barge on ropes; water on barge and barge on water. Since all the forces in the left column are forces acting on the ship, all the forces in the right column are forces exerted by the ship. Therefore, every entry in the column starts with 'ship'.

If you looked at the forces you found, you would have discovered that there was a downward force of gravity on the ship that was not canceled out by any upward force. This strategy guarantees that you will find any contact force acting on the object, although it will not help you find non-contact forces. Analyze the forces she is participating in at the moment her feet are on the cliff and she pushes off.

The only horizontal force on her is the cliff force, which is not canceled by any other force and will therefore cause Cindy to accelerate to the right. You simply draw a picture of an object with arrows representing the forces acting on it. A In the case of a barge going down a canal, I mentioned the "buoyant" or "hydrostatic" force that prevents the boat from sinking.

Analyze the forces in which the ball participates during the short time it is in contact with the side of the table. C The earth's gravitational force on you, i.e. your weight, is always equal to your mass.

## Transmission of Forces by Low-Mass

If the rope has negligible mass, all the forces are equal to +T or −T, where T, the tension, is a single number. For example, if we think of the two halves of the string as two objects, then each half exerts a force on the other half. If we imagine the string as consisting of many small parts, then each segment transfers a force to the next segment, and if the string has very little mass, then all the forces are equal.

There are many forces within the string, some in one direction and some in the other direction, and their magnitudes are only approximately equal. The concept of tension makes sense only as a general, approximate statement of how large all forces are. If a rope is passed over a pulley or around some other object, then the tension throughout the rope is approximately equal as long as there is not much friction.

A rod or stick can be treated in much the same way as a string, but it is possible to have either compression or tension. Since tension is not a type of force, the force that a rope exerts on another object must be of a specific type, such as static friction, kinetic friction, or a normal force. If you hold your dog's leash with your hand through the loop, then the force the leash exerts on your hand is a normal force: it is the force that prevents the leash from taking up the same space as your hand.

When you grasp a plain end of a rope, the force between the rope and your hand is a frictional force. Many people would describe the car's engine as the one that exerts the force that accelerates the car, but the engine is part of the car, so that's impossible: objects cannot exert forces on themselves. What actually happens is that the power from the engine is transferred through the transmission to the axles and then through the tires to the road.

According to Newton's third law, there will thus be a forward force from the road on the tires which accelerates the car. A When you step on the gas pedal, the force of your foot is transferred within the meaning of the word used in this section.

## Objects Under Strain

For example, if you press down on the hood of a car, it will drop by an amount directly proportional to the force. But the behavior of the car would not be so mathematically simple if you dropped a boulder on the bonnet!). A A car is connected to its axles through large, stiff springs called shock absorbers or "shocks". Although we have only discussed Hooke's law above in the case of stretching a spring, a car's shock is constantly undergoing both stretching and compression.

In this situation, how would you interpret the positive and negative signs in Hooke's law.

## Simple Machines: the Pulley

Each instance of Newton's third law involves exactly two objects and exactly two forces that are of the same type. The direction of the force is in the direction that would tend to stop or prevent sliding. Hooke's law states that the stretch or compression of the object is proportional to the force exerted on it.

2 The earth is attracted to an object with a force equal and opposite to the force of the earth on the object. This problem depends on the results of problems 14 and 16, the solutions of which are in the back of the book. Note that the paradox is not resolved by considering the force of the batsman's hands on the bat.

When a force acts on an object, it has no effect on the part of the object's motion that is perpendicular to the force. In the examples above, the vertical force of gravity had no effect on the horizontal movements of the objects. In the case of the projectile's motion, the force involved is gravity, so we can more specifically say that the vertical acceleration is 9.8 m/s2, regardless of the horizontal motion.

In the example of the ball being blown sideways, why doesn't the ball take longer to get there since it has to travel a greater distance. C Consider the example of the bullet being dropped at the same moment that another bullet is fired from a gun. What would the motion of the two bullets look like to a jet pilot flying side by side in the same direction as the shot bullet and at the same horizontal speed.

If all three components of the total force on an object are zero, it will remain in the same state of motion. They therefore think that the object will accelerate and move in the direction of the stronger force.

## Techniques for Adding Vectors

A When doing graphical addition of vectors, it matters which vector you start with and which vector you start from the other vector's point. B If you add a vector of magnitude 1 to a vector of magnitude 2, what magnitudes are possible for the vector sum. However, if we perform the same operations in coordinate system i/3, rotated 45 degrees with respect to the previous one, we find.

The result of the operation depends on which coordinate system we use, and since the two versions of R have different lengths (one is zero and the other is non-zero), they do not simply represent the same answer expressed in two different coordinate systems. Such an operation will never be useful in physics because experiments show that physics works the same way no matter which way we orient the laboratory building. The useful vector operations, such as addition and scalar multiplication, are rotation invariant, i.e. comes out the same regardless of the orientation of the coordinate system.

A vector is a quantity that has both magnitude (amount) and direction in space, as opposed to a scalar, which has no direction. In two dimensions, a vector can be represented by two components or by magnitude and direction. The two main operations on vectors are addition of a vector to a vector and multiplication of a vector by a scalar.

In graphical terms, this is equivalent to drawing the vectors as two arrows laid from tip to tail and drawing the sum vector from the tail of the first vector to the tip of the second. 4 A machinist drills holes in a piece of aluminum according to the diagram in the figure. She starts with the top hole, then moves to the hole on the left, and then to the hole on the right.

Since this is a high precision job, it ends up moving in the direction and angle it needs to return to the top hole and checks that it ends up in the same place. What is the distance and direction from the right hole to the top hole.

The Acceleration Vector

The Force Vector and Simple

R