Torque: Kinetic Energy Essay Example

The torque you created on the door is smaller than it would have been had you pushed the correct side (away from its hinges). Note that the force applied, F, and the moment arm, r, are independent of the object.

Furthermore, a force applied at the pivot point will cause no torque since the moment arm would be zero (r = O). Another way of xpressing the above equation is that torque is the product of the magnitude of the force and the perpendicular distance from the force to the axis of rotation (i. e. the pivot point). Let the force acting on an object be broken up into its tangential

In order to lift the lever, you apply a force F to point P, which is a distance r away from the axis of rotation, as illustrated below. Suppose the lever is very heavy and resists your efforts to lift it.

If you want to put all you can into lifting this lever, what should you do? Simple intuition would suggest, first of all, that you should lift with all your strength. Second, you should grab onto the end of the lever, and not a point near its axis of rotation. Third, you should lift in a direction that is perpendicular to the lever: if you pull very hard away from the wall or push very hard toward the wall, the lever won't rotate at all.

Let's summarize. In order to maximize torque, you need to: 1. Maximize the magnitude of the force, F, that you apply to the lever.

2. Maximize the distance, r, from the axis of rotation of the point on

the lever to which you apply the force. 3. Apply the force in a direction perpendicular to the lever. We can apply these three requirements to an equation for torque, : In this equation, is the angle made between the vector for the applied force and the lever. Torque Defined in Terms of Perpendicular Components There's another way of thinking about torque that may be a bit more intuitive than the definition provided above.

Torque is the product of the distance of the applied force from the axis of rotation and the component of the applied force that is perpendicular to the lever arm. Or, alternatively, torque is the product of the applied force and the component of the length of the lever arm that runs perpendicular to the applied force. We can express these relations mathematically as follows: where and are defined below. Torque Defined as a Vector Quantity Torque, like angular velocity and angular acceleration, is a vector quantity.

Most precisely, it is the cross product of the displacement vector, r, from the axis of otation to the point where the force is applied, and the vector for the applied force, To determine the direction of the torque vector, use the right-hand rule, curling your fingers around from the r vector over to the F vector. In the example of lifting the lever, the torque would be represented by a vector at O pointing out of the page. Example I A student exerts a force of 50 N on a lever at a distance 0. 4 m from its axis of rotation.

The student pulls at an angle that is 60„0 above the

lever arm. What is the torque experienced by the lever arm? I Let's plug these values into the first equation we saw for torque:

This vector has its tail at the axis of rotation, and, according to the right-hand rule, points out of the page. Energy Basics: I Issac Says: "Let's Learn about Potential and Kinetic Energy! " I Potential Energy: Potential energy exists whenever an object which has mass has a position within a force field. The most everyday example of this is the position of objects in the earth's gravitational field.

The potential energy of an object in this case is given by the relation: PE = mgh where * PE = Energy (in Joules) * m = mass (in kilograms) * g = gravitational acceleration of the earth (9. 8 m/sec2) * h = height above arth's surface (in meters) Kinetic Energy: Kinetic Energy exists whenever an object which has mass is in motion with some velocity. Everything you see moving about has kinetic energy. The kinetic energy of an object in this case is given by the relation: KE = (1 /2)mv2 * KE = Energy (in Joules) * v = velocity (in meters/sec) Conservation of Energy This principle asserts that in a closed system energy is conserved. This principle will be tested by you, using the experimental apparatus below.

In the case of an object in free fall. When the object is at rest at some height, h, then all of its energy is PE.

As the object falls and accelerates due to the earth's gravity, PE is converted into KE. When the object strikes the ground, so that PE=O,

the all of the energy has to be in the form of KE and the object is moving it at its maximum velocity. (In this case we are ignoring air resistance). These concepts are merely an outgrowth of Newton's second law as discussed in an earlier unit.

Newton's second law (Fnet = m  a) stated that the acceleration of an object is directly proportional to the net force acting upon the object and inversely proportional to the mass of the object. When combined with he definition of acceleration (a = change in velocity / time), the following equalities result. If both sides of the above equation are multiplied by the quantity t, a new equation results. collisions during this unit. To truly understand the equation, it is important to understand its meaning in words. In words, it could be said that the force times the time equals the mass times the change in velocity.

In physics, the quantity Force  time is known as impulse. And since the quantity mv is the momentum, the quantity  must be the change in momentum. The equation really says that the Impulse =

Change in momentum One focus of this unit is to understand the physics of collisions. The physics of collisions are governed by the laws of momentum; and the first law which we discuss in this unit is expressed in the above equation. The equation is known as the impulse-momentum change equation. The law can be expressed this way: In a collision, an object experiences a force for a specific amount of time which results in a change in momentum.

The result of the force acting for the

given amount of time is that the object's mass either speeds up or slows down (or changes direction). The mpulse experienced by the object equals the change in momentum of the object. In equation form, F  = m  v. What Is Linear Momentum? Linear momentum is a vector quantity defined as the product of an object's mass, m, and its velocity, v.

Linear momentum is denoted by the letter p and is called "momentum" for short: Note that a bodys momentum is always in the same direction as its velocity vector. The units of momentum are kg  m/s. Fortunately, the way that we use the word momentum in everyday life is consistent with the definition of momentum in physics. For example, we say that a BMW driving 20 miles per hour has less momentum than he same car speeding on the highway at 80 miles per hour.

Additionally, we know that if a large truck and a BMW travel at the same speed on a highway, the truck has a greater momentum than the BMW, because the truck has greater mass. Our everyday usage reflects the definition given above, that momentum is proportional to mass and velocity. Linear Momentum and Newton's Second Law In Chapter 3, we introduced Newton's Second Law as F = ma. However, since acceleration can be expressed as , we could equally well express Newton's Second Law as F = .

Substituting p for mv, we find an expression of Newton's Second Law in erms of momentum: In fact, this is the form in which Newton first expressed his Second Law. It is more flexible than F = ma because it

can be used to analyze systems where not Just the velocity, but also the mass of a body changes, as in the case of a rocket burning fuel. Impulse The above version of Newton's Second Law can be rearranged to define the impulse, J, delivered by a constant force, F. Impulse is a vector quantity defined as the product of the force acting on a body and the time interval during which the force is exerted.

If the force changes during the time interval, F is the average net force over that time interval.

The impulse caused by a force during a specific time interval is equal to the bodys change of momentum during that time interval: impulse, effectively, is a The unit of impulse is the same as the unit of momentum, kg  m/s. Example I A soccer player kicks a 0. 1 kg ball that is initially at rest so that it moves with a velocity of 20 m/s. What is the impulse the player imparts to the ball? If the player's foot was in contact with the ball for 0.

01 s, what was the force exerted by the player's foot on the ball? What is the impulse the player imparts to the ball? Since impulse is simply the change in momentum, we need to calculate the ifference between the ball's initial momentum and its final momentum. Since the ball begins at rest, its initial velocity, and hence its initial momentum, is zero. Its final momentum is: Because the initial momentum is zero, the ball's change in momentum, and hence its impulse, is 2 kg  m/s. What was the force exerted by

the player's foot on the ball? Impulse is the product of the force exerted and the time interval over which it was exerted. It follows, then, that . Since we have already calculated the impulse and have been given the time interval, this is an easy calculation: Impulse and Graphs

SAT II Physics may also present you with a force vs.

time graph, and ask you to calculate the impulse. There is a single, simple rule to bear in mind for calculating the impulse in force vs. time graphs: The impulse caused by a force during a specific time interval is equal to the area underneath the force vs. time graph during the same interval. If you recall, whenever you are asked to calculate the quantity that comes from multiplying the units measured by the y-axis with the units measured by the x-axis, you do so by calculating the area under the graph for the relevant interval.

I What is the impulse delivered by the force graphed in the figure above between t = O and t = 5? | The impulse over this time period equals the area of a triangle of height 4 and base 4 plus the area ofa rectangle of height 4 and width 1.

A quick calculation shows us that the impulse is: Work When we are told that a person pushes on an object with a certain force, we only know how hard the person pushes: we don't know what the pushing accomplishes. Work, W, a scalar quantity that measures the product of the force exerted on an object and the resulting displacement of that object, is a measure

of what an applied orce accomplishes. The harder you push an object, and the farther that object or by the object or person exerting the force, on the object on which the force is acting. Most simply, work is the product of force times displacement. However, as you may have remarked, both force and displacement are vector quantities, and so the direction of these vectors comes into play when calculating the work done by a given force. Work is measured in units of Joules 0), where 1 J = 1 N m = 1  m2/s2.

Energy Energy is one of the central concepts of physics, and one of the most difficult to define.

One of the reasons we have such a hard time defining it is because it appears in so many different forms. There is the kinetic and potential energy of kinematic motion, the thermal energy of heat reactions, the chemical energy of your discman batteries, the mechanical energy of a machine, the elastic energy that helps you launch rubber bands, the electrical energy that keeps most appliances on this planet running, and even mass energy, the strange phenomenon that Einstein discovered and that has been put to such devastating effect in the atomic bomb. This is only a cursory list: energy takes on an even wider variety of forms.

Energy, like work, is measured in Joules 0).

In fact, work is a measure of the transfer of energy. However, there are forms of energy that do not involve work. For instance, a box suspended from a string is doing no work, but it has gravitational potential energy that will turn into work as

soon as the string is cut. We will look at some of the many forms of energy shortly. First, let's examine the important law of conservation of energy. Conservation of Energy As the name suggests, the law of conservation of energy tells us that the energy in the universe is constant.

Energy cannot be made or destroyed, only changed from ne form to another form. Energy can also be transferred via a force, or as heat. For instance, let's return to the example mentioned earlier of the box hanging by a string. As it hangs motionless, it has gravitational potential energy, a kind of latent energy.

When we cut the string, that energy is converted into kinetic energy, or work, as the force of gravity acts to pull the box downward. When the box hits the ground, that kinetic energy does not simply disappear. Rather, it is converted into sound and heat energy: the box makes a loud thud and the impact between the ground and the box generates a bit of heat.

Forms of Energy Though energy is always measured in Joules, and though it can always be defined as a capacity to do work, energy manifests itself in a variety of different forms. These various forms pop up all over SAT II Physics, and we will look at some additional forms of energy when we discuss electromagnetism, relativity, and a number of other specialized topics.

For now, we will focus on the kinds of energy you'll find in mechanics problems. Kinetic Energy Kinetic energy is the energy a body in motion has by virtue of its motion. We define work. For instance, a

cue ball on a pool table can use its motion to do work on the ight ball.

When the cue ball strikes the eight ball, the cue ball comes to a stop and the eight ball starts moving. This occurs because the cue ball's kinetic energy has been transferred to the eight ball. There are many types of kinetic energy, including vibrational, translational, and rotational. Translational kinetic energy, the main type, is the energy of a particle moving in space and is defined in terms of the particle's mass, m, and velocity, v: For instance, a cue ball of mass 0. 5 kg moving at a velocity of 2 m/s has a kinetic energy of 1/2 (0. 5 kg)(2 m/s)2 = 1 J.

The Work-Energy Theorem