PHY1604 ASSIGNMENT 4 2021

PHY1604
ASSIGNMENT 4 2021


QUESTION 1

𝐿𝑒𝑡: 𝑅1 = 𝑏𝑟𝑒𝑎𝑡ℎ𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑝𝑎𝑐𝑒𝑐𝑟𝑎𝑓𝑡

𝑅2 = 𝑏𝑟𝑒𝑎𝑡ℎ𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 𝑎𝑡 𝑒𝑎𝑟𝑡ℎ



∆𝑡 = 𝛾∆𝑡𝑝

1
𝛾=
2
√1 − 𝑣2
𝑐

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑟𝑒𝑎𝑡ℎ𝑠
𝑅1 =
∆𝑡𝑝

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑟𝑒𝑎𝑡ℎ𝑠
𝑅2 =
∆𝑡

𝑇ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑟𝑒𝑎𝑡ℎ𝑠 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑐ℎ𝑎𝑛𝑔𝑒 , 𝑏𝑢𝑡 𝑡ℎ𝑒 𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙𝑠 𝑎𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡.

𝑅1 ∆𝑡𝑝 = 𝑅2 ∆𝑡

𝑅1 ∆𝑡𝑝
𝑅2 =
∆𝑡
∆𝑡𝑝 ∆𝑡𝑝 1
𝑅2 = 𝑅1 ∴ =
∆𝑡 ∆𝑡 𝛾

𝑅1
𝑅2 =
𝛾



𝑅1 = 8.0 𝑏𝑟𝑒𝑎𝑡ℎ𝑠 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒

1
𝛾= ∴ 𝑣 = 0.975𝑐
2
√1 − 𝑣2
𝑐

, 1
𝛾=
2
√1 − (0.975𝑐)
𝑐2
1
𝛾=
2𝑐 2
√1 − (0.975)
2
𝑐
1
𝛾=
√1 − (0.975)2

𝛾 = 4.5



𝑅1
𝑅2 =
𝛾

8
𝑅2 =
4.5

𝑅2 = 1.78 𝑏𝑟𝑒𝑎𝑡ℎ𝑠 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒



𝐴𝑠 𝑚𝑜𝑛𝑖𝑡𝑜𝑟𝑒𝑑 𝑜𝑛 𝑒𝑎𝑟𝑡ℎ 𝑡ℎ𝑒 𝑏𝑟𝑒𝑎𝑡ℎ𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 = 1.78 𝑏𝑟𝑒𝑎𝑡ℎ𝑠 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒


QUESTION 2

∆𝑡 = 𝛾∆𝑡𝑝

∆𝑡
𝑊𝑒 𝑎𝑟𝑒 𝑡𝑜𝑙𝑑: ∆𝑡𝑝 =
2

∆𝑡 = 𝛾∆𝑡𝑝

∆𝑡
∆𝑡 = 𝛾 ( )
2

𝛾=2



𝑝𝑟𝑒𝑙 = 𝛾𝑚𝑣⃗

𝑚𝑣⃗ = 𝑛𝑜𝑛𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑖𝑠𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 1.3 × 1013 𝑘𝑔. 𝑚/𝑠

𝑝𝑟𝑒𝑙 = 2(1.3 × 1013 )

𝑝𝑟𝑒𝑙 = 2.6 × 1013 𝑘𝑔. 𝑚/𝑠

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑖𝑠𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑝𝑎𝑐𝑒𝑠𝑐𝑎𝑓𝑡 = 2.6 × 1013 𝑘𝑔. 𝑚/𝑠