The findings indicate T1 = 131.4 [N] and T2 = 261 [N].
The distance covered during the acceleration phase is d = 214.38 m. Given parameters include the acceleration of the object, a = -6.8 m/s², initial speed, u = 54 m/s, and final speed, v = 0. The equation for acceleration is defined as a = (v - u) / t. Therefore, rearranging gives t = (v - u) / a, resulting in t = (0 - 54) / (-6.8) = 7.94 s. The average speed of the object is V = (54 + 0)/2 = 27 m/s. The displacement is calculated as d = V x t = 27 x 7.94 = 214.38 m. Thus, the total distance traveled during that period of acceleration is 214.38 m.
Answer:
Explanation:
The length of a vector refers to its magnitude.
For a vector
R = a•i + b•j + c•k
The magnitude can be calculated using
|R|= √(a²+b²+c²)
Applying this formula to each given vector yields the following results.
(a) 2i + 4j + 3k
The length is
L = √(2²+4²+3²)
L = √(4+16+9)
L = √29
L = 5.385 unit
(b) 5i − 2j + k
Note that k represents 1k
The length is
L = √(5²+(-2)²+1²)
Because, -×- = +
L = √(25+4+1)
L = √30
L = 5.477 unit
(c) 2i − k
As there is no j component, it means that the j component is 0
L = 2i + 0j - 1k
The length is
L = √(2²+0²+(-1)²)
L = √(4+0+1)
L = √5
L = 2.236 unit
(d) 5i
Similarly, without a j-component and k-component
L = 5i + 0j + 0k
The length is
L = √(5²+0²+0²)
L = √(25+0+0)
L = √25
L = 5 unit
(e) 3i − 2j − k
The length is
L = √(3²+(-2)²+(-1)²)
L = √(9+4+1)
L = √14
L = 3.742 unit
(f) i + j + k
The length is
L = √(1²+1²+1²)
L = √(1+1+1)
L = √3
L = 1.7321 unit
Answer:
The required energy remains identical in both scenarios since the specific heat capacity (Cp) does not change with varying pressure.
Explanation:
Given;
initial temperature, t₁ = 50 °C
final temperature, t₂ = 80 °C
Temperature change, ΔT = 80 °C - 50 °C = 30 °C
Pressure for scenario one = 1 atm
Pressure for scenario two = 3 atm
The energy needed in both scenarios is expressed as;
Where;
Cp denotes specific heat capacity, which only varies with temperature and remains unaffected by pressure.
Hence, the energy required remains the same for both scenarios since specific heat capacity (Cp) is pressure-independent.
