Other Harmonic Systems - AP Physics 1
Card 0 of 24
You push on a door with a force of 1.3 N at an angle of 45 degrees to the surface and at a distance of 0.5 m from the hinges. What is the torque produced?
You push on a door with a force of 1.3 N at an angle of 45 degrees to the surface and at a distance of 0.5 m from the hinges. What is the torque produced?
Tap to see back →
To calculate torque, this equation is needed:
Next, identify the given information:
Plug these numbers into the equation to determine the torque:
To calculate torque, this equation is needed:
Next, identify the given information:
Plug these numbers into the equation to determine the torque:
If a mass on the end of a string of length 8 cm is pulled 30 degrees away from vertical, what will its speed be when the string is vertically alligned if the mass is released from rest?
If a mass on the end of a string of length 8 cm is pulled 30 degrees away from vertical, what will its speed be when the string is vertically alligned if the mass is released from rest?
Tap to see back →
We can determine the vertical components by using some geometry.
Since this problem boils down to being a problem of conservation of energy, we can state that
Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified:
is equal to the height of the mass above 0 m; therefore, by referring to the diagram, we can determine that 
. By plugging this in and rearranging the equation, we can solve for the speed of the mass when the string is vertically aligned:
We can determine the vertical components by using some geometry.
Since this problem boils down to being a problem of conservation of energy, we can state that
Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified:
A ball with mass 5 kg is attached to a spring and is released 10 meters from equilibrium. After some time, the ball passes the equilibrium point moving at 
. What is the spring constant (
) of the spring?
A ball with mass 5 kg is attached to a spring and is released 10 meters from equilibrium. After some time, the ball passes the equilibrium point moving at
Tap to see back →
When the object is released, it has no kinetic energy (it isn't moving) and a potential energy of
When the object passes through the equilibrium point, it has no potential energy (
) and a kinetic energy of
Due to the conservation of energy, these two quantities must be equal to each other:
When the object is released, it has no kinetic energy (it isn't moving) and a potential energy of
When the object passes through the equilibrium point, it has no potential energy (
Due to the conservation of energy, these two quantities must be equal to each other:
A 30 kg weight attached to a spring is at equilibrium lying horizontally on a table. The spring is lifted up and is stretched by 80 cm before the weight is lifted off the table. What is this spring's spring constant (
)?
A 30 kg weight attached to a spring is at equilibrium lying horizontally on a table. The spring is lifted up and is stretched by 80 cm before the weight is lifted off the table. What is this spring's spring constant (
Tap to see back →
First, we should convert 80 centimeters to 0.8 meters.
We know the force applied to the weight by gravity is
The force applied by the spring in the opposite direction must be equal to this:
First, we should convert 80 centimeters to 0.8 meters.
We know the force applied to the weight by gravity is
The force applied by the spring in the opposite direction must be equal to this:
Instead of using a second hand to count seconds, a watchmaker decides to construct a simple harmonic system involving a mass and a spring suspended from a table.
Ignoring the effects of gravity, if the spring the watchmaker selects has a spring constant of 
, how large of a mass in kilograms should he attach to the spring such that the harmonic system does not oscillate too slow or too fast?
Instead of using a second hand to count seconds, a watchmaker decides to construct a simple harmonic system involving a mass and a spring suspended from a table.
Ignoring the effects of gravity, if the spring the watchmaker selects has a spring constant of
Tap to see back →
The angular velocity of the harmonic system is equal to the square root of the spring constant over the mass:
Since we need the angular velocity to be 
and we are given the spring constant as 
, then we can set up an equation:
The angular velocity of the harmonic system is equal to the square root of the spring constant over the mass:
Since we need the angular velocity to be
The position of a 
mass in an oscillating spring-mass system is given by the following equation:
, where 
is measured in 
, and 
is measured in 
.
What is the velocity equation of the system as a function of time?
The position of a
What is the velocity equation of the system as a function of time?
Tap to see back →
The velocity equation can be found by differentiating the position equation.
Here, we made use of the chain rule in taking the derivative.
The velocity equation can be found by differentiating the position equation.
Here, we made use of the chain rule in taking the derivative.
You push on a door with a force of 1.3 N at an angle of 45 degrees to the surface and at a distance of 0.5 m from the hinges. What is the torque produced?
You push on a door with a force of 1.3 N at an angle of 45 degrees to the surface and at a distance of 0.5 m from the hinges. What is the torque produced?
Tap to see back →
To calculate torque, this equation is needed:
Next, identify the given information:
Plug these numbers into the equation to determine the torque:
To calculate torque, this equation is needed:
Next, identify the given information:
Plug these numbers into the equation to determine the torque:
If a mass on the end of a string of length 8 cm is pulled 30 degrees away from vertical, what will its speed be when the string is vertically alligned if the mass is released from rest?
If a mass on the end of a string of length 8 cm is pulled 30 degrees away from vertical, what will its speed be when the string is vertically alligned if the mass is released from rest?
Tap to see back →
We can determine the vertical components by using some geometry.
Since this problem boils down to being a problem of conservation of energy, we can state that
Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified:
is equal to the height of the mass above 0 m; therefore, by referring to the diagram, we can determine that . By plugging this in and rearranging the equation, we can solve for the speed of the mass when the string is vertically aligned:
We can determine the vertical components by using some geometry.
Since this problem boils down to being a problem of conservation of energy, we can state that
Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified:
A ball with mass 5 kg is attached to a spring and is released 10 meters from equilibrium. After some time, the ball passes the equilibrium point moving at . What is the spring constant () of the spring?
A ball with mass 5 kg is attached to a spring and is released 10 meters from equilibrium. After some time, the ball passes the equilibrium point moving at
Tap to see back →
When the object is released, it has no kinetic energy (it isn't moving) and a potential energy of
When the object passes through the equilibrium point, it has no potential energy () and a kinetic energy of
Due to the conservation of energy, these two quantities must be equal to each other:
When the object is released, it has no kinetic energy (it isn't moving) and a potential energy of
When the object passes through the equilibrium point, it has no potential energy (
Due to the conservation of energy, these two quantities must be equal to each other:
A 30 kg weight attached to a spring is at equilibrium lying horizontally on a table. The spring is lifted up and is stretched by 80 cm before the weight is lifted off the table. What is this spring's spring constant ()?
A 30 kg weight attached to a spring is at equilibrium lying horizontally on a table. The spring is lifted up and is stretched by 80 cm before the weight is lifted off the table. What is this spring's spring constant (
Tap to see back →
First, we should convert 80 centimeters to 0.8 meters.
We know the force applied to the weight by gravity is
The force applied by the spring in the opposite direction must be equal to this:
First, we should convert 80 centimeters to 0.8 meters.
We know the force applied to the weight by gravity is
The force applied by the spring in the opposite direction must be equal to this:
Instead of using a second hand to count seconds, a watchmaker decides to construct a simple harmonic system involving a mass and a spring suspended from a table.
Ignoring the effects of gravity, if the spring the watchmaker selects has a spring constant of , how large of a mass in kilograms should he attach to the spring such that the harmonic system does not oscillate too slow or too fast?
Instead of using a second hand to count seconds, a watchmaker decides to construct a simple harmonic system involving a mass and a spring suspended from a table.
Ignoring the effects of gravity, if the spring the watchmaker selects has a spring constant of
Tap to see back →
The angular velocity of the harmonic system is equal to the square root of the spring constant over the mass:
Since we need the angular velocity to be and we are given the spring constant as , then we can set up an equation:
The angular velocity of the harmonic system is equal to the square root of the spring constant over the mass:
Since we need the angular velocity to be
The position of a mass in an oscillating spring-mass system is given by the following equation:
, where is measured in , and is measured in .
What is the velocity equation of the system as a function of time?
The position of a
What is the velocity equation of the system as a function of time?
Tap to see back →
The velocity equation can be found by differentiating the position equation.
Here, we made use of the chain rule in taking the derivative.
The velocity equation can be found by differentiating the position equation.
Here, we made use of the chain rule in taking the derivative.
You push on a door with a force of 1.3 N at an angle of 45 degrees to the surface and at a distance of 0.5 m from the hinges. What is the torque produced?
You push on a door with a force of 1.3 N at an angle of 45 degrees to the surface and at a distance of 0.5 m from the hinges. What is the torque produced?
Tap to see back →
To calculate torque, this equation is needed:
Next, identify the given information:
Plug these numbers into the equation to determine the torque:
To calculate torque, this equation is needed:
Next, identify the given information:
Plug these numbers into the equation to determine the torque:
If a mass on the end of a string of length 8 cm is pulled 30 degrees away from vertical, what will its speed be when the string is vertically alligned if the mass is released from rest?
If a mass on the end of a string of length 8 cm is pulled 30 degrees away from vertical, what will its speed be when the string is vertically alligned if the mass is released from rest?
Tap to see back →
We can determine the vertical components by using some geometry.
Since this problem boils down to being a problem of conservation of energy, we can state that
Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified:
is equal to the height of the mass above 0 m; therefore, by referring to the diagram, we can determine that . By plugging this in and rearranging the equation, we can solve for the speed of the mass when the string is vertically aligned:
We can determine the vertical components by using some geometry.
Since this problem boils down to being a problem of conservation of energy, we can state that
Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified:
A ball with mass 5 kg is attached to a spring and is released 10 meters from equilibrium. After some time, the ball passes the equilibrium point moving at . What is the spring constant () of the spring?
A ball with mass 5 kg is attached to a spring and is released 10 meters from equilibrium. After some time, the ball passes the equilibrium point moving at
Tap to see back →
When the object is released, it has no kinetic energy (it isn't moving) and a potential energy of
When the object passes through the equilibrium point, it has no potential energy () and a kinetic energy of
Due to the conservation of energy, these two quantities must be equal to each other:
When the object is released, it has no kinetic energy (it isn't moving) and a potential energy of
When the object passes through the equilibrium point, it has no potential energy (
Due to the conservation of energy, these two quantities must be equal to each other:
A 30 kg weight attached to a spring is at equilibrium lying horizontally on a table. The spring is lifted up and is stretched by 80 cm before the weight is lifted off the table. What is this spring's spring constant ()?
A 30 kg weight attached to a spring is at equilibrium lying horizontally on a table. The spring is lifted up and is stretched by 80 cm before the weight is lifted off the table. What is this spring's spring constant (
Tap to see back →
First, we should convert 80 centimeters to 0.8 meters.
We know the force applied to the weight by gravity is
The force applied by the spring in the opposite direction must be equal to this:
First, we should convert 80 centimeters to 0.8 meters.
We know the force applied to the weight by gravity is
The force applied by the spring in the opposite direction must be equal to this:
Instead of using a second hand to count seconds, a watchmaker decides to construct a simple harmonic system involving a mass and a spring suspended from a table.
Ignoring the effects of gravity, if the spring the watchmaker selects has a spring constant of , how large of a mass in kilograms should he attach to the spring such that the harmonic system does not oscillate too slow or too fast?
Instead of using a second hand to count seconds, a watchmaker decides to construct a simple harmonic system involving a mass and a spring suspended from a table.
Ignoring the effects of gravity, if the spring the watchmaker selects has a spring constant of
Tap to see back →
The angular velocity of the harmonic system is equal to the square root of the spring constant over the mass:
Since we need the angular velocity to be and we are given the spring constant as , then we can set up an equation:
The angular velocity of the harmonic system is equal to the square root of the spring constant over the mass:
Since we need the angular velocity to be
The position of a mass in an oscillating spring-mass system is given by the following equation:
, where is measured in , and is measured in .
What is the velocity equation of the system as a function of time?
The position of a
What is the velocity equation of the system as a function of time?
Tap to see back →
The velocity equation can be found by differentiating the position equation.
Here, we made use of the chain rule in taking the derivative.
The velocity equation can be found by differentiating the position equation.
Here, we made use of the chain rule in taking the derivative.
You push on a door with a force of 1.3 N at an angle of 45 degrees to the surface and at a distance of 0.5 m from the hinges. What is the torque produced?
You push on a door with a force of 1.3 N at an angle of 45 degrees to the surface and at a distance of 0.5 m from the hinges. What is the torque produced?
Tap to see back →
To calculate torque, this equation is needed:
Next, identify the given information:
Plug these numbers into the equation to determine the torque:
To calculate torque, this equation is needed:
Next, identify the given information:
Plug these numbers into the equation to determine the torque:
If a mass on the end of a string of length 8 cm is pulled 30 degrees away from vertical, what will its speed be when the string is vertically alligned if the mass is released from rest?
If a mass on the end of a string of length 8 cm is pulled 30 degrees away from vertical, what will its speed be when the string is vertically alligned if the mass is released from rest?
Tap to see back →
We can determine the vertical components by using some geometry.
Since this problem boils down to being a problem of conservation of energy, we can state that
Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified:
is equal to the height of the mass above 0 m; therefore, by referring to the diagram, we can determine that . By plugging this in and rearranging the equation, we can solve for the speed of the mass when the string is vertically aligned:
We can determine the vertical components by using some geometry.
Since this problem boils down to being a problem of conservation of energy, we can state that
Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified: