Answer:
The distance covered by the minutes hand is 39.60 cm.
Explanation:
Note: A clock has a circular shape, where the minutes hand acts as the radius, and its motion creates an arc.
Length of an arc is calculated as ∅/360(2πr)
L = ∅/360(2πr).................... Equation 1π
Here, L represents the arc’s length, ∅ is the angle made by the arc, and r is the arc’s radius.
Given: ∅ = 252°, r = 9 cm, π = 3.143.
Upon substituting these values into equation 1,
L = 252/360(2×3.143×9)
L = 0.7×2×3.143×9
L = 39.60 cm.
Thus, the distance traversed by the minutes hand is 39.60 cm.
The force can be determined using the equation F (force) = mass * acceleration. The unit of measurement, N (Newton), is equivalent to kilogram-meter/seconds2.
Thus, F= 1300 kg * 1.07 m/s2 = 1391 N.
The resultant value is 1391 N.
Answer:
The water level increases more when the cube is above the raft before it sinks.
Explanation:
The principle involved is based on Archimedes' theory, which states that immersing an object in water will raise the initial water level. This means that the height of the water in the container increases. The increase in water volume corresponds to the volume of the submerged object.
We can consider two scenarios: when the steel cube rests on the raft and when it settles at the pool's bottom.
When the cube rests at the pool’s bottom, the volume will indeed rise, and we can ascertain this using the cube's volume.
Vc = 0.45*0.45*0.45 = 0.0911 [m^3]
When an object floats, it's because the densities of the object and water are in equilibrium.
![Ro_{H2O}=R_{c+r}\\where:\\Ro_{H2O}= water density = 1000 [kg/m^3]\\Ro_{c+r}= combined density cube + raft [kg/m^3]](https://tex.z-dn.net/?f=Ro_%7BH2O%7D%3DR_%7Bc%2Br%7D%5C%5Cwhere%3A%5C%5CRo_%7BH2O%7D%3D%20water%20density%20%3D%201000%20%5Bkg%2Fm%5E3%5D%5C%5CRo_%7Bc%2Br%7D%3D%20combined%20density%20cube%20%2B%20raft%20%5Bkg%2Fm%5E3%5D)
The formula for density is:
Ro = m/V
where:
m= mass [kg]
V = volume [m^3]
The buoyant force can be calculated with this equation:
![F_{B}=W=Ro_{H20}*g*Vs\\W = (200+730)*9.81\\W=9123.3[N]\\\\9123=1000*9.81*Vs\\Vs = 0.93 [m^3]](https://tex.z-dn.net/?f=F_%7BB%7D%3DW%3DRo_%7BH20%7D%2Ag%2AVs%5C%5CW%20%3D%20%28200%2B730%29%2A9.81%5C%5CW%3D9123.3%5BN%5D%5C%5C%5C%5C9123%3D1000%2A9.81%2AVs%5C%5CVs%20%3D%200.93%20%5Bm%5E3%5D)
Vs > Vc indicates that the combined volume of the raft and the cube exceeds that of the cube alone resting at the bottom of the pool. Hence, when the cube is positioned above the raft, the water level rises more before it becomes submerged.