Question

At Harris Teeter, James buys 2 cans of soup, 2 boxes of Oreo cookies and 2 oranges. James uses only one plastic grocery bag, which supports 90 N before ripping. Assume all three objects are uniform and solid throughout.

Dimensions of orange: Diameter = 5.00 cm ρ = 7.87 x 102 kg/m3

Dimensions of Oreo Box: Length: 24.00 cm Width: 10.00 cm Height: 18.00 cm ρ = 3.32 x 102 kg/m3
Dimensions of soup can: Diameter = 6.00 cm Height= 10.00 cm ρ = 1.06 x 104 kg/m3

What is the mass of 2 cans of soup?

What is the mass of 2 boxes of Oreo cookies?

What is the mass of 2 orange?

What is the total mass added into the bag?

What is the net force that the objects exert on the bag?

Will the bag rip? Will James be able to buy one more item? If yes which one?

Answer 1

the mass of 2 cans of soup :

Diameter = 6.00 cm = 0.06 m

radius r = 0.06 / 2 = 0.03 m

Height h = 10.00 cm = 0.1 m

ρ = 1.06 X 10⁴ kg / m³

density ρ = mass m / volume V

volume of the can is cylinder V = 1 / 3 X 3.14 X r² X h

V = 1 / 3 X 3.14 X 0.03² X 0.1

V = 9.32 X 10^-5 m³

mass of each can is = ρ X V

m = 1.06 X 10⁴ X 9.32 X 10^-5

m = 9.872 X 10^-1 Kg

m = 0.98792 Kg

the mass of 2 cans of soup is 2 X 0.98792 = 1.97584 Kg

the mass of 2 boxes of Oreo cookies :

Length: 24.00 cm = 0.24 m

Width: 10.00 cm = 0.1 m

Height: 18.00 cm = 0.18 m

ρ = 3.32 X10² kg/m³

mass of oreo box is = ρ X V

= ρ X L X b X h

= 3.32 X10² X 0.24 X 0.1 X 0.18

mass of oreo box is = 1.43424 Kg

the mass of 2 boxes of Oreo cookies is = 2 X 1.43424

the mass of 2 boxes of Oreo cookies is = 2.86848 Kg

the mass of 2 orange :

Diameter = 5.00 cm = 0.05m

radius r = 0.025 m

ρ = 7.87 X 10² kg/m³

mass of orange = ρ X V

mass of orange = ρ X 4/3 X 3.14 X r³

mass of orange = 7.87 X 10² X 1.33 X 3.14 X 0.025³

mass of orange = 0.051 Kg

mass of 2 orange = 2 X 0.051

mass of 2 orange = 0.102 Kg

the mass of 2 cans of soup is 2 X 0.98792 = 1.97584 Kg

and

the mass of 2 boxes of Oreo cookies is = 2.86848 Kg

and

mass of 2 orange = 0.102 Kg

total mass added into the bag is = 0.102 +1.97584 + 2.86848

total mass added into the bag is = 4.94632 Kg

the net force that the objects exert on the bag is F

F = total mass m X g

F = 4.94632 X 9.8

the net force that the objects exert on the bag is F = 48.47 N

given force 96 N but the given objects excerting force is only 48.47 N

it is exactly half of the given force.

no bag will bear the force..

james can add the mass which excerts nearly same force like the above items.