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How heavy is 0.343750 pounds?

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It's about as heavy as a Billiard Ball.
In other words, the weight of a Billiard Ball is 1.0454545454546 times 0.343750 pounds.
(American-style, WPA specifications)
Per the World Pool-Billiard Association, a billiard ball weight must weigh between 0.343750 pounds and 0.3750 pounds. According to legend, the difficulty in obtaining elephant ivory for the manufacture of billiard balls in the 19th century inspired the search for a replacement material, which led to the development of the first industrial plastic.
It's about as heavy as a Puck (Hockey).
In other words, the weight of a Puck (Hockey) is 1.0454545454546 times 0.343750 pounds.
(Ice hockey)
A standard ice hockey puck weighs between 0.343750 pounds and 0.3750 pounds. Hockey pucks can be shot or passed at speeds of up to 160 kph (99 mph) during games.
It's about one-and-one-tenth times as heavy as a Baseball.
In other words, 0.343750 pounds is 1.0731707317073 times the weight of a Baseball, and the weight of a Baseball is 0.93181818181820 times that amount.
(MLB rules)
Per Major League Baseball rules, a baseball must weigh between 0.31250 pounds and 0.3281250 pounds. A major league pitcher can throw a baseball at up to 150 kph (91 mph) (with a fastball pitch), with record-setting pitches as fast as 171 kph (106 mph).
It's about one-and-one-fifth times as heavy as a Battery (D).
In other words, 0.343750 pounds is 1.150 times the weight of a Battery (D), and the weight of a Battery (D) is 0.870 times that amount.
(Alkaline)
A "D" size battery weighs 0.2980 pounds. The D size battery is the oldest of the modern battery sizes, first invented by the National Carbon Company in 1898.
It's about four-fifths as heavy as a Hamster.
In other words, the weight of a Hamster is 1 times 0.343750 pounds.
(for Syrian hamster, a.k.a. golden hamster, a.k.a. Mesocricetus auratus; adult)
An adult Syrian hamster has a typical weight of about 0.40 pounds. Known for transporting food in the pouches of their cheeks so that they can bury it later, some hamsters can store up to 60 pounds of food in their borrows.
It's about one-and-seven-tenths times as heavy as a Deck of Cards.
In other words, the weight of a Deck of Cards is 0.590 times 0.343750 pounds.
(ISO 216 B8 size, a.k.a. "poker size" 63 x 88 mm, 52-card deck)
A deck of 52 ISO 216 B8-size playing cards weighs 0.210 pounds. Utilizing nearly 3,700 decks, the record-holding largest card tower was built in early 2010, stood over 3.5 m (11 ft), and weighed over 500 pounds.
It's about half as heavy as a Human Heart.
In other words, the weight of a Human Heart is 2 times 0.343750 pounds.
(human; adult)
The average human heart weighs about 0.680 pounds. Each minute, the heart pumps between 10 and 20 liters (3 to 5 gallons) of blood through its chambers.