1. A baseball player decides to show his skills by catching a 0.142-kg baseball dropped from the top of a 96-m tall building. What is the speed (in m/s) of the baseball just before it strikes his glove?
2. A child and sled with a combined mass of 35.9 kg slide down a frictionless hill. The sled starts from rest and has acquired a speed of 3.7 m/s by the time it reaches the bottom of the hill. What is the height (in m) of the hill? Enter your answer, accurate to the fourth decimal place.
3. A 39.3-kg high jumper leaves the ground with a speed of 5.7 m/s. How high (in m) can he leap? Enter your answer, accurate to the third decimal place.
4. Find the height (in m) from which you would have to drop your textbook so that it would have a speed of 14.2 m/s just before it hits the floor?
Tuesday, January 29, 2008
Potential and kinetic energy
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 earth'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
where
KE = Energy (in Joules)
m = mass (in kilograms)
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, h=0 so that PE=0, 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).
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 earth'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
where
KE = Energy (in Joules)
m = mass (in kilograms)
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, h=0 so that PE=0, 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).
Practice questions pict only one number pass it on feb 3
1. Determine the momentum of a ...
a. 60-kg halfback moving eastward at 9 m/s.
b. 1000-kg car moving northward at 20 m/s.
c. 40-kg freshman moving southward at 2 m/s.
2. A car possesses 20 000 units of momentum. What would be the car's new momentum if ...
a. its velocity were doubled.
b. its velocity were tripled.
c. its mass were doubled (by adding more passengers and a greater load)
d. both its velocity were doubled and its mass were doubled.
a. 60-kg halfback moving eastward at 9 m/s.
b. 1000-kg car moving northward at 20 m/s.
c. 40-kg freshman moving southward at 2 m/s.
2. A car possesses 20 000 units of momentum. What would be the car's new momentum if ...
a. its velocity were doubled.
b. its velocity were tripled.
c. its mass were doubled (by adding more passengers and a greater load)
d. both its velocity were doubled and its mass were doubled.
impulse and momentum
The Impulse-Momentum Change Theorem
Momentum
The sports announcer says "Going into the all-star break, the Chicago White Sox have the momentum." The headlines declare "Chicago Bulls Gaining Momentum." The coach pumps up his team at half-time, saying "You have the momentum; the critical need is that you use that momentum and bury them in this third quarter."
Momentum is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop. A team that has a lot of momentum is really on the move and is going to be hard to stop. Momentum is a physics term; it refers to the quantity of motion that an object has. A sports team which is on the move has the momentum. If an object is in motion (on the move) then it has momentum.
Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum which an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.
Momentum = mass • velocity
In physics, the symbol for the quantity momentum is the lower case "p". Thus, the above equation can be rewritten as
p = m • v
where m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.
The units for momentum would be mass units times velocity units. The standard metric unit of momentum is the kg•m/s. While the kg•m/s is the standard metric unit of momentum, there are a variety of other units which are acceptable (though not conventional) units of momentum. Examples include kg•mi/hr, kg•km/hr, and g•cm/s. In each of these examples, a mass unit is multiplied by a velocity unit to provide a momentum unit. This is consistent with the equation for momentum.
Momentum is a vector quantity. As discussed in an earlier unit, a vector quantity is a quantity which is fully described by both magnitude and direction. To fully describe the momentum of a 5-kg bowling ball moving westward at 2 m/s, you must include information about both the magnitude and the direction of the bowling ball. It is not enough to say that the ball has 10 kg•m/s of momentum; the momentum of the ball is not fully described until information about its direction is given. The direction of the momentum vector is the same as the direction of the velocity of the ball. In a previous unit, it was said that the direction of the velocity vector is the same as the direction which an object is moving. If the bowling ball is moving westward, then its momentum can be fully described by saying that it is 10 kg•m/s, westward. As a vector quantity, the momentum of an object is fully described by both magnitude and direction.
From the definition of momentum, it becomes obvious that an object has a large momentum if either its mass or its velocity is large. Both variables are of equal importance in determining the momentum of an object. Consider a Mack truck and a roller skate moving down the street at the same speed. The considerably greater mass of the Mack truck gives it a considerably greater momentum. Yet if the Mack truck were at rest, then the momentum of the least massive roller skate would be the greatest. The momentum of any object which is at rest is 0. Objects at rest do not have momentum - they do not have any "mass in motion." Both variables - mass and velocity - are important in comparing the momentum of two objects.
The momentum equation can help us to think about how a change in one of the two variables might affect the momentum of an object. Consider a 0.5-kg physics cart loaded with one 0.5-kg brick and moving with a speed of 2.0 m/s. The total mass of loaded cart is 1.0 kg and its momentum is 2.0 kg•m/s. If the cart was instead loaded with three 0.5-kg bricks, then the total mass of the loaded cart would be 2.0 kg and its momentum would be 4.0 kg•m/s. A doubling of the mass results in a doubling of the momentum.
Similarly, if the 2.0-kg cart had a velocity of 8.0 m/s (instead of 2.0 m/s), then the cart would have a momentum of 16.0 kg•m/s (instead of 4.0 kg•m/s). A quadrupling in velocity results in a quadrupling of the momentum. These two examples illustrate how the equation p = m•v serves as a "guide to thinking" and not merely a "plug-and-chug recipe for algebraic problem-solving."
Momentum
The sports announcer says "Going into the all-star break, the Chicago White Sox have the momentum." The headlines declare "Chicago Bulls Gaining Momentum." The coach pumps up his team at half-time, saying "You have the momentum; the critical need is that you use that momentum and bury them in this third quarter."
Momentum is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop. A team that has a lot of momentum is really on the move and is going to be hard to stop. Momentum is a physics term; it refers to the quantity of motion that an object has. A sports team which is on the move has the momentum. If an object is in motion (on the move) then it has momentum.
Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum which an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.
Momentum = mass • velocity
In physics, the symbol for the quantity momentum is the lower case "p". Thus, the above equation can be rewritten as
p = m • v
where m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.
The units for momentum would be mass units times velocity units. The standard metric unit of momentum is the kg•m/s. While the kg•m/s is the standard metric unit of momentum, there are a variety of other units which are acceptable (though not conventional) units of momentum. Examples include kg•mi/hr, kg•km/hr, and g•cm/s. In each of these examples, a mass unit is multiplied by a velocity unit to provide a momentum unit. This is consistent with the equation for momentum.
Momentum is a vector quantity. As discussed in an earlier unit, a vector quantity is a quantity which is fully described by both magnitude and direction. To fully describe the momentum of a 5-kg bowling ball moving westward at 2 m/s, you must include information about both the magnitude and the direction of the bowling ball. It is not enough to say that the ball has 10 kg•m/s of momentum; the momentum of the ball is not fully described until information about its direction is given. The direction of the momentum vector is the same as the direction of the velocity of the ball. In a previous unit, it was said that the direction of the velocity vector is the same as the direction which an object is moving. If the bowling ball is moving westward, then its momentum can be fully described by saying that it is 10 kg•m/s, westward. As a vector quantity, the momentum of an object is fully described by both magnitude and direction.
From the definition of momentum, it becomes obvious that an object has a large momentum if either its mass or its velocity is large. Both variables are of equal importance in determining the momentum of an object. Consider a Mack truck and a roller skate moving down the street at the same speed. The considerably greater mass of the Mack truck gives it a considerably greater momentum. Yet if the Mack truck were at rest, then the momentum of the least massive roller skate would be the greatest. The momentum of any object which is at rest is 0. Objects at rest do not have momentum - they do not have any "mass in motion." Both variables - mass and velocity - are important in comparing the momentum of two objects.
The momentum equation can help us to think about how a change in one of the two variables might affect the momentum of an object. Consider a 0.5-kg physics cart loaded with one 0.5-kg brick and moving with a speed of 2.0 m/s. The total mass of loaded cart is 1.0 kg and its momentum is 2.0 kg•m/s. If the cart was instead loaded with three 0.5-kg bricks, then the total mass of the loaded cart would be 2.0 kg and its momentum would be 4.0 kg•m/s. A doubling of the mass results in a doubling of the momentum.
Similarly, if the 2.0-kg cart had a velocity of 8.0 m/s (instead of 2.0 m/s), then the cart would have a momentum of 16.0 kg•m/s (instead of 4.0 kg•m/s). A quadrupling in velocity results in a quadrupling of the momentum. These two examples illustrate how the equation p = m•v serves as a "guide to thinking" and not merely a "plug-and-chug recipe for algebraic problem-solving."
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