2.6 Forces
REGENTS PHYSICS: Forces
PRACTICE PROBLEM
Two lifeguards pull on ropes attached to a raft.
Scenario 1: Both pull in the same direction, net external force is 321 N to the right.
Scenario 2: Both pull in opposite directions, net external force is 152 N to the left.
Tasks:
a) Draw a Free Body Diagram for both situations and find the magnitude of the larger individual force.
b) Determine the magnitude of the smaller individual force.
SOLUTION
Equations:
For Scenario 1:
F_net = F1 + F2
F1 + F2 = 321 N
For Scenario 2:
F_net = F1 - F2
F1 - F2 = -152 N
Solving Simultaneous Equations:
Substitute F1 from Scenario 1 into Scenario 2:
F1 = 321 N - F2
Plug into Scenario 2 equation:
(321 N - F2) - F2 = -152 N
321 N - 2F2 = -152 N
2F2 = 473 N
F2 = 236.5 N
F1 = 321 N - 236.5 N = 84.5 N
AIM: Circular Motion
Key Questions:
What is circular motion?
How to quantify circular motion?
What is the period of circular motion?
What is centripetal acceleration?
What is centripetal force?
How is centripetal force used to explain circular motion?
ANNOUNCEMENTS
No Lab on Thursday.
Exam 1 has been returned.
Exam 2 Date: Tuesday, October 29 (Cumulative: Questions from previous topics).
Topics to Review:
Distance, Displacement, Speed, Velocity, Acceleration
Newton’s Laws
Mass vs Weight
Vector Addition
Bring Calculator and Reference Table to the exam.
PRACTICE: Newton’s Second Law and FBD
Problem Statement:
A crate is pushed to the right at 18 N, accelerating at 3 m/s² with a frictional force of 6 N acting on it.
Tasks:
Draw a Free Body Diagram (FBD).
Determine mass of the crate.
Calculate the Normal Force.
SOLUTION:
Net Force Calculation:
F_net = ma:
12 N = (m)(3 m/s²) --> m = 4 kg
Gravitational Force:
F_g = mg = (4 kg)(9.8 m/s²) = 39.2 N
Normal Force:
Normal Force (F_N) = 39.2 N
DISCUSSION
Can an object moving at constant speed accelerate?
Yes, if direction of the velocity is changing (e.g., circular motion).
Justification using Newton’s Laws:
Objects in circular motion change direction, implying acceleration due to a net force.
CIRCULAR MOTION & NEWTON’S LAWS
Key concepts:
Velocity is a vector (magnitude + direction).
Acceleration is the rate of change of velocity.
Acceleration is directly proportional to force (Newton’s Second Law).
Conclusion:
Objects in circular motion are constantly accelerating due to a net inward force.
CIRCULAR MOTION PRINCIPLES
Centripetal Force:
The net force that causes circular motion.
Causes centripetal acceleration towards the center of the path.
CIRCULAR MOTION DEMO
Consider acceleration vectors for
An object accelerating from rest and
An object moving in a circle.
PERIOD OF CIRCULAR MOTION
Definition: Time taken for one complete trip around a circular path.
Symbol: T; measured in seconds.
Relation: T = t/n, where t is total time, and n is number of trips.
EXAMPLES OF PERIODIC MOTION
Examples of periodic movements:
Pendulum swings, wave motion, and circular paths.
Practice Problems:
Fly wings flap 121 times/second → T = 0.00826 seconds.
Pendulum completing 33 cycles in 11 seconds → T = 0.33 seconds.
REGENTS PHYSICS: Forces
PRACTICE PROBLEM
Two lifeguards pull on ropes attached to a raft.
Scenario 1: Both pull in the same direction,
Net external force: 321 N to the right (indicating a combination of both lifeguards' effort in the same direction).
Interpretation: This results in a stronger overall force, as both forces add together.
Scenario 2: Both pull in opposite directions,
Net external force: 152 N to the left (indicating that one lifeguard's force is greater than the other's, yielding a net force in the direction of the stronger pull).
Interpretation: The opposing forces partially balance each other, producing a smaller net external force.
Tasks:
(a) Draw a Free Body Diagram (FBD) for both situations, representing forces exerted on the raft vectorially.
Find the magnitude of the larger individual force: This requires solving for the two forces based on the net forces observed in each scenario.
(b) Determine the magnitude of the smaller individual force.
SOLUTION
Equations:
For Scenario 1:[ F_{net} = F_1 + F_2 ][ F_1 + F_2 = 321 ext{ N} ]
For Scenario 2:[ F_{net} = F_1 - F_2 ][ F_1 - F_2 = -152 ext{ N} ]
Solving Simultaneous Equations:
Substitute F1 from Scenario 1 into Scenario 2:[ F_1 = 321 ext{ N} - F_2 ]
Plug this into the Scenario 2 equation:[ (321 ext{ N} - F_2) - F_2 = -152 ext{ N} ]
Simplify:[ 321 ext{ N} - 2F_2 = -152 ext{ N} ]
Rearranging gives:[ 2F_2 = 473 ext{ N} ]
Thus,[ F_2 = 236.5 ext{ N} ]
Calculating F1 gives:[ F_1 = 321 ext{ N} - 236.5 ext{ N} = 84.5 ext{ N} ]
AIM: Circular Motion
Key Questions:
What is circular motion?
Definition: Motion of an object in a circular path.
How to quantify circular motion?
Includes variables such as radius, angular velocity, and tangential speed.
What is the period of circular motion?
The time taken for one complete cycle around the circle (denoted by T).
What is centripetal acceleration?
Acceleration directed towards the center of a circular path, caused by the net inward force.
What is centripetal force?
The net force that acts on an object moving in a circular path, directed towards the center.
How is centripetal force used to explain circular motion?
It is the necessary force that keeps an object moving along a curved trajectory.
ANNOUNCEMENTS
No Lab on Thursday.
Exam 1 has been returned.
Exam 2 Date: Tuesday, October 29 (Cumulative: Questions from previous topics).
Topics to Review:
Distance, Displacement, Speed, Velocity, Acceleration
Newton’s Laws
Mass vs Weight
Vector Addition
Reminder:
Bring Calculator and Reference Table to the exam.
PRACTICE: Newton’s Second Law and Free Body Diagram
Problem Statement:
A crate is pushed to the right at 18 N, accelerating at 3 m/s² with a frictional force of 6 N acting on it.
Tasks:
Draw a Free Body Diagram (FBD) to illustrate forces acting on the crate.
Determine the mass of the crate.
Calculate the Normal Force acting on the crate.
SOLUTION:
Net Force Calculation:
Using Newton’s Second Law:[ F_{net} = ma: ][ 12 ext{ N} = (m)(3 ext{ m/s}²) \rightarrow m = 4 ext{ kg} ]
Gravitational Force:
[ F_g = mg = (4 ext{ kg})(9.8 ext{ m/s}²) = 39.2 ext{ N} ]
Normal Force:
The Normal Force (F_N), which acts perpendicular to the surface, counteracts the gravitational force, thus:[ F_N = 39.2 ext{ N} ]
DISCUSSION
Can an object moving at constant speed accelerate?
Yes, if the direction of the velocity is changing (e.g., in circular motion).
Justification using Newton’s Laws:
Objects in circular motion experience a continuous change in direction, implying acceleration due to a net inward force.
CIRCULAR MOTION & NEWTON’S LAWS
Key Concepts:
Velocity is a vector: It incorporates both magnitude and direction.
Acceleration is the rate of change of velocity: It reflects how quickly an object's speed or direction changes.
Acceleration is directly proportional to force (as stated in Newton’s Second Law): The more force applied, the more acceleration produced.
Conclusion: Objects in circular motion are under constant acceleration due to the presence of a net inward force.
CIRCULAR MOTION PRINCIPLES
Centripetal Force:
The net force that causes circular motion; it creates centripetal acceleration directed toward the center of the path of motion.
CIRCULAR MOTION DEMO
Consider acceleration vectors for an object that accelerates from rest versus one that moves in a circle, illustrating principles of velocity and acceleration in different contexts.
PERIOD OF CIRCULAR MOTION
Definition:
Time taken for one complete trip around a circular path, symbolized as T and measured in seconds.
Relation:
[ T = \frac{t}{n}, \text{ where } t \text{ is total time, and } n \text{ is number of trips.} ]
EXAMPLES OF PERIODIC MOTION
Examples of periodic movements:
Pendulum swings
Wave motion
Circular paths
Practice Problems:
Fly wings flap 121 times/second → T = 0.00826 seconds.
Pendulum completing 33 cycles in 11 seconds → T = 0.33 seconds.