AP Physics 1 Notes
Circular Motion, Torque, and Oscillations
Name: ______________________
Springs and Pendulums
Forces on Springs Revisited: The force required to elongate a spring increases as the spring gets longer. The magnitude of this force is determined by F = kx, where k is the spring constant given in N/m and x is the distance the spring is elongated.
Example:
1. What force is required to pull a spring, having a spring constant of 10 N/m, back 3 meters?
2. What is the spring constant of a spring that stretches 0.5 meters when a force of 35 N is applied to it?
3. A 2 kg mass is hung on a spring which elongates the spring 2 meters. a. Draw a free body diagram of the mass on the spring.
b. What is the spring constant on this spring?
Springs, like pendulums, can also be used to keep time. Each of these dives have a specific equation that can be seen on your equation sheet. m is the mass of the object on the spring, k is the spring constant, l is the length of the pendulum, T is the period of the device, and g is the acceleration due to gravity.
Examples:
1. A 5 kg mass is hung on a spring having a spring constant of 10 N/m. The spring is then set into oscillation. What is the period of this oscillation? How much time does it take for the mass to move from its highest point to its lowest point?
Periodic Motion
Periodic Motion: Motion that repeats itself in a regular time interval.
Would the mass on the spring, the pendulum, and a person doing pushups be examples of periodic motion?
Harmonic Motion: Periodic motion that accelerates toward an equilibrium point.
Would the mass on the spring, the pendulum, and a person doing pushups be examples of harmonic motion?
Simple Harmonic Motion: Harmonic motion that does not have a change in amplitude or frequency. Would the mass on the spring, the pendulum, and a person doing pushups be examples of simple harmonic motion?
1. Watch the mass on the spring oscillate. Sketch a graph of the position of the mass’s height as a function of time:
y
t
2. Let’s label some times on the graph, then answer the following questions. a. What is the period of the oscillation?
b. At what time on the graph is the displacement at its: i. Maximum?
ii. Minimum?
c. At what time on the graph is the speed at its: i. Maximum?
ii. Minimum?
d. At what time on the graph is the acceleration at its: i. Maximum?
Torque and Rotational Equilibrium
Torques are to rotation as forces are to linear motion. Torques are essentially the effect on objects that cause them to rotate. The torque equation can be found on your equation sheet.
Examples:
1. How much torque is applied when a 100 N force applied perpendicularly to the handle turns a bolt from the end of a 0.25 meter long wrench?
2. A 3 meter long shovel is used to lift a stone with a perpendicular force of 500 N from the end of the shovel. How much torque was applied by the force?
Like forces, torques can often cause equilibrium. In those cases, the sum of the torques clockwise will equal the sum of the torques counterclockwise.
Examples:
1. A 30 N force is applied to the left side of a seesaw 2 meters from the pivot point. What force should be applied at 1 meter to the right of the pivot point to keep the seesaw from rotating?
Rotation Concept Questions
1. A 2 kg beam supports a 20 kg mass and a 75 kg mass on each end as diagramed below. Draw the approximate point on the beam where we could pivot the beam so that it would balance. Explain why you chose that location.
1. The following system is comprised of a thin, low-mass beam supported by a rope at its center and having three masses hanging on it as diagramed below such that the system does not rotate. Determine the value of the hanging mass.
Rope
2x x x
2. A 25 kg uniform plank is supported by two ladders as diagramed below. How far from the ladder on the right can the 90 kg person walk before tipping the plank over?
90 kg
6 meters 4meters
Ladder Ladder
3. A 6 meter long uniform beam is pivoted in its center and has a 20 N force applied at an angle of 35° as diagramed below. Where and in what direction on the left side of the beam should another 20 N force be applied perpendicular to the beam to prevent it from rotating?
20 N 35°
Centripetal Acceleration and Centripetal Force
2 kg beam
20 kg 75 kg
6 meter beam beam
7 kg ? kg 3 kg
r
1. A mass on a string spins around at a constant speed, does it accelerate? Why?
v 2. How do we calculate this acceleration?
3. If we want to calculate the force applied on the object spinning around, we can combine Newton’s Second Law with this centripetal acceleration.
Example 1:
1. Draw a top-view free body diagram of the forces acting on a bob as it spins horizontally around tied to a string.
2. How much tension in a string is required to spin a 0.25 kg mass around with a constant speed of 5 m/s with a radius of 2 m?
3. Will the tension increase or decrease if all other factors stay the same except the length of the spin radius increases?
Example 2:
1. Draw an aerial-view free body diagram of the forces acting on a car as it rounds a curve.
2. What frictional force is required to cause a 1000 kg car to go around 80 meter radius curve at a speed of 11 m/s?
3. What minimal coefficient of friction between the tires and the road is required to keep the car from skidding?
The same centripetal acceleration can be used to describe satellites going around in circular orbits.
1. Draw a free-body diagram of a satellite as it orbits the earth.
2. Use Newton’s second law to form an expression for the speed needed to orbit the earth at a given distance.
Example: A satellite is to be set in circular orbit around the earth at a distance of 1.75 x 107 meters
from the center of the earth. At what speed will the satellite have to travel to maintain this orbit?
