Once the object has left contact with whatever held or threw it, the object is in free-fall. Under these circumstances, the motion is one-dimensional and has constant acceleration of magnitude g. We will also represent vertical displacement with the symbol y and use x for horizontal displacement. A person standing on the edge of a high cliff throws a rock straight up with an initial velocity of The rock misses the edge of the cliff as it falls back to earth.
Calculate the position and velocity of the rock 1. We are asked to determine the position y at various times. It is reasonable to take the initial position y 0 to be zero.
This problem involves one-dimensional motion in the vertical direction. We use plus and minus signs to indicate direction, with up being positive and down negative. Since up is positive, and the rock is thrown upward, the initial velocity must be positive too. The acceleration due to gravity is downward, so a is negative. It is crucial that the initial velocity and the acceleration due to gravity have opposite signs.
Opposite signs indicate that the acceleration due to gravity opposes the initial motion and will slow and eventually reverse it. Since we are asked for values of position and velocity at three times, we will refer to these as y 1 and v 1 ; y 2 and v 2 ; and y 3 and v 3. Identify the knowns. Identify the best equation to use.
Plug in the known values and solve for y 1. The rock is 8. It could be moving up or down; the only way to tell is to calculate v 1 and find out if it is positive or negative. However, it has slowed from its original The results are summarized in Table 1 and illustrated in Figure 3. Figure 3. Vertical position, vertical velocity, and vertical acceleration vs. Notice that velocity changes linearly with time and that acceleration is constant.
Misconception Alert! Notice that the position vs. It is easy to get the impression that the graph shows some horizontal motion—the shape of the graph looks like the path of a projectile. But this is not the case; the horizontal axis is time, not space.
The actual path of the rock in space is straight up, and straight down. The interpretation of these results is important. Notice that when the rock is at its highest point at 1. Note that the values for y are the positions or displacements of the rock, not the total distances traveled.
Finally, note that free-fall applies to upward motion as well as downward. Both have the same acceleration—the acceleration due to gravity, which remains constant the entire time. Astronauts training in the famous Vomit Comet, for example, experience free-fall while arcing up as well as down, as we will discuss in more detail later.
A simple experiment can be done to determine your reaction time. Have a friend hold a ruler between your thumb and index finger, separated by about 1 cm. Note the mark on the ruler that is right between your fingers. Have your friend drop the ruler unexpectedly, and try to catch it between your two fingers. Note the new reading on the ruler. Assuming acceleration is that due to gravity, calculate your reaction time. What happens if the person on the cliff throws the rock straight down, instead of straight up?
To explore this question, calculate the velocity of the rock when it is 5. Similarly, the initial velocity is downward and therefore negative, as is the acceleration due to gravity.
We expect the final velocity to be negative since the rock will continue to move downward. Choose the kinematic equation that makes it easiest to solve the problem. We will plug y 1 in for y. The negative root is chosen to indicate that the rock is still heading down. Note that this is exactly the same velocity the rock had at this position when it was thrown straight upward with the same initial speed.
See Example 1 and Figure 5 a. This is not a coincidental result. Because we only consider the acceleration due to gravity in this problem, the speed of a falling object depends only on its initial speed and its vertical position relative to the starting point. For example, if the velocity of the rock is calculated at a height of 8.
Here both signs are meaningful; the positive value occurs when the rock is at 8. It has the same speed but the opposite direction. Figure 5. The arrows are velocity vectors at 0, 1. Note that at the same distance below the point of release, the rock has the same velocity in both cases. Another way to look at it is this: In Example 1, the rock is thrown up with an initial velocity of It rises and then falls back down. That is, it has the same speed on its way down as on its way up.
Friction depends on the hardness or roughness of the contacting surfaces. Fluid friction depends on the viscosity the thickness of the fluid. In the case of sliding, friction is reduced at very high relative speeds. However, in the case of fluid friction, friction increases with increase in relative speed of movement. To stop an object in motion, a force must act on it in the opposite direction of motion.
The force that opposes the motion of the object is called the frictional force. Look at the diagram. At first the block is at rest, then the pushing force keeps the block moving. As the block slides over the surface, the frictional force acts on it in the opposite direction.
A unit of friction is a Newton, as forces are measured using Newtons. Friction generally depends on weight of the object and nature of the surface between the moving object and supporting surface. Different types of motion of the object gives rise to different types of friction. Generally, there are 4 types of friction. They are static friction, sliding friction, rolling friction, and fluid friction.
The next sections will explore these forces and when they are applied. Static friction exists between a stationary object and the surface on which it is resting. Term net force. Definition sum of all forces acting on an object. Term acceleration. Term If you increase the force on an object, its acceleration. Definition also increases.
Term 2 ways to increase acceleration. Definition increase force and mass. Term If you increase the mass on an object, its acceleration. Term inertia. Definition resistance to a change in motion. Term amount of inertia an object has depends on its. Definition mass. Term the work of pulling a box will be. Definition easier if the person uses a ramp.
Term ramps make work easier by. Definition exerting smaller input force even though the distance is longer. Term efficiency of machine. Term ideal mechanical advantage of a ramp is its mechanical advantage without. Term efficiency. Definition compares the output work to the input work.
Term machine. Definition device that allows you to do work in a way that is easier. Term actual mechanical advantage. Definition mechanical advantage that a machine provides in a real situation. Term output force. Definition force the machine exerts on an object. Term output work. Definition output force x the output distance. Term mechanical advantage. Term input force.
Definition force you exert on a machine. Term input work. Definition input force x the input distance. Term ideal mechanical advantage. Definition mechanical advantage of a machine without friction. Term work. Definition force x distance, measured in Nm also called a Joule. Term joule. Definition SI unit of work when you exert a force of 1 newton to move an object a distance of 1 meter. Term power. Definition the rate at which work is done, equals the amount of work done on an object in a unit of time.
Term inclined plane. Definition simple machine - flat, sloped or slanted surface - examples are ramps. Term wedge. Definition simple machine - thick at one end and tapers at the other triangle shaped , example is an axe.
Term screw. Definition simple machine - inclined plane wrapped around a cylinder to form a spiral. Term lever.
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