Mathematics
Grade 11
15 min
Which customary unit of weight is appropriate?
Which customary unit of weight is appropriate?
What you'll learn
- Identify whether to use ounces or pounds to measure the weight of different objects with 80% accuracy.
- Explain why a specific customary unit (ounce or pound) is the most appropriate unit to measure the weight of a given object in at least 2 out of 3 examples.
- Apply knowledge of ounces and pounds to estimate the weight of 3 common classroom objects using the appropriate unit (ounce or pound) with reasonable accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Model periodic changes in apparent weight using sinusoidal functions.
Resolve a weight vector on an inclined plane into its parallel and perpendicular components using sine and cosine.
Calculate the magnitude of forces related to weight in various physical systems.
Select the most appropriate customary unit of weight (ounce, pound, or ton) based on the calculated magnitude of a trigonometric component of force.
Interpret the amplitude of a trigonometric weight function as the maximum deviation from static weight.
Analyze how the angle of inclination affects the trigonometric components of a weight vector.
Represent a weight vector in the complex plane and analyze its components using the trigonometric form of a complex number.
Ever feel lighter at the t...
2
Key Concepts & Vocabulary
TermDefinitionExample
Weight Vector ResolutionThe process of breaking down the force vector of weight into two or more component vectors, typically parallel and perpendicular to a surface, using trigonometric functions.A 100-pound box on a ramp inclined at 30° has a weight component pulling it down the ramp of 100 sin(30°) = 50 pounds.
Apparent WeightThe force an object exerts on its support. It is equal to the object's static weight only when at rest or moving at a constant velocity; it changes with vertical acceleration.In an elevator accelerating upwards, your apparent weight is greater than your static weight. This can be modeled by W_app = mg + ma.
Sinusoidal Weight ModelA mathematical model using a sine or cosine function to represent a situation where apparent weight changes c...
3
Core Formulas
Weight Component Formulas (Inclined Plane)
For an object with weight W on a surface inclined at an angle θ to the horizontal: F_parallel = W sin(θ) and F_normal = W cos(θ)
Use these formulas to find the force component pulling the object down the incline (parallel) and the force component pressing the object into the surface (normal/perpendicular). θ is the angle of the incline itself.
Sinusoidal Apparent Weight Model
W_app(t) = W_static + A cos(ωt + φ)
This models the apparent weight (W_app) over time (t) for an object in simple harmonic motion. W_static is the weight at rest, A is the amplitude (maximum change in force), ω is the angular frequency, and φ is the phase shift.
Unit Selection Thresholds
If Magnitude M < 1 lb, consider ounces. If 1 lb ≤ M < 2000 lbs...
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
The apparent weight of a payload during launch is modeled by W(t) = 1500 + 600cos(πt/2) lbs. At time t=0, the weight vector is represented as a complex number z = r(cos(90°) + i sin(90°)). What is the most appropriate customary unit to express the magnitude, r?
A.Ounces
B.Pounds
C.Tons
D.The unit changes with time.
Challenging
A 100 lb object is on a 35° incline. Consider the normal force (F_normal) and the parallel force (F_parallel). What is the most appropriate customary unit to express the absolute difference between the magnitudes of these two forces?
A.Ounces
B.Pounds
C.Tons
D.The difference is zero.
Challenging
A truck weighing 8,000 lbs is on an adjustable ramp. At approximately what minimum angle of inclination (θ) does the force component parallel to the ramp (F_parallel) become large enough that 'tons' is the most appropriate customary unit to express it?
A.14.5°
B.30.0°
C.45.0°
D.1.4°
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Trigonometric functions
Mathematics for other grades
Frequently asked questions
What grade level is "Which customary unit of weight is appropriate?"?
Which customary unit of weight is appropriate? is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Which customary unit of weight is appropriate??
You'll be able to: Identify whether to use ounces or pounds to measure the weight of different objects with 80% accuracy; Explain why a specific customary unit (ounce or pound) is the most appropriate unit to measure the weight of a given object….
Is "Which customary unit of weight is appropriate?" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Which customary unit of weight is appropriate??
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.