Solution: This solution uses an origin located at the center of the lower can. The right triangle has a hypotenuse of 2r. The horizontal leg has a length of (w – 2r). Using Pythagorean Theorem, the vertical leg is: dvert = √√(2r)² - (w – 2r)² – - Square out the 2nd term and clean up: dvert = √√4wr w² - Torque balance equation: TCCW - TCW = 0 Let 2(mg) be the total weight of both cans, which can be viewed as acting at the CM of the 2 cans. Plug in using Tr₁F: w-2r = 0 (Nwall) (√4wr – w²) – (2(mg)) (1-2) = - Cans in a Box N wall W CMQ 2(mg) N wall N floor Jamie puts 2 beverage cans in a cooler. Ignore friction. Each can has a mass m and a radius r. The width of the cooler is w. Each wall exerts a normal force Nwall as shown. Hint: Use the right triangle shown. Choose an origin and calculate torques. 9 10 r พ m Nwall 0.491 3.12cm 10.5cm N kg Type your answer... r พ m Nwall 3.42cm 10.1cm 4.13N kg 0.777

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 12E: Find the height of a storage tank in the shape of a right circular cylinder that as a circumference...
Question
Solution:
This solution uses an origin located at the center of the
lower can.
The right triangle has a hypotenuse of 2r. The
horizontal leg has a length of (w – 2r). Using
Pythagorean Theorem, the vertical leg is:
dvert = √√(2r)² - (w – 2r)²
–
-
Square out the 2nd term and clean up:
dvert = √√4wr w²
-
Torque balance equation:
TCCW - TCW = 0
Let 2(mg) be the total weight of both cans, which can
be viewed as acting at the CM of the 2 cans. Plug in
using Tr₁F:
w-2r
= 0
(Nwall) (√4wr – w²) – (2(mg)) (1-2) =
-
Transcribed Image Text:Solution: This solution uses an origin located at the center of the lower can. The right triangle has a hypotenuse of 2r. The horizontal leg has a length of (w – 2r). Using Pythagorean Theorem, the vertical leg is: dvert = √√(2r)² - (w – 2r)² – - Square out the 2nd term and clean up: dvert = √√4wr w² - Torque balance equation: TCCW - TCW = 0 Let 2(mg) be the total weight of both cans, which can be viewed as acting at the CM of the 2 cans. Plug in using Tr₁F: w-2r = 0 (Nwall) (√4wr – w²) – (2(mg)) (1-2) = -
Cans in a Box
N
wall
W
CMQ
2(mg)
N
wall
N
floor
Jamie puts 2 beverage cans in a
cooler. Ignore friction.
Each can has a mass m and a radius
r. The width of the cooler is w. Each
wall exerts a normal force Nwall as
shown.
Hint: Use the right triangle shown.
Choose an origin and calculate
torques.
9
10
r
พ
m
Nwall
0.491
3.12cm 10.5cm
N
kg
Type your answer...
r
พ
m
Nwall
3.42cm
10.1cm
4.13N
kg
0.777
Transcribed Image Text:Cans in a Box N wall W CMQ 2(mg) N wall N floor Jamie puts 2 beverage cans in a cooler. Ignore friction. Each can has a mass m and a radius r. The width of the cooler is w. Each wall exerts a normal force Nwall as shown. Hint: Use the right triangle shown. Choose an origin and calculate torques. 9 10 r พ m Nwall 0.491 3.12cm 10.5cm N kg Type your answer... r พ m Nwall 3.42cm 10.1cm 4.13N kg 0.777
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