The required lift force is approximately 866.92 N. To determine this, we first establish the shark's mass at 92 kg and its density at 1040 kg/m³. The volume of the shark is calculated by dividing mass by density, yielding 0.08846 m³. The buoyant force acting on the shark is then determined by multiplying the volume by the density of water and gravity, resulting in a lift force of 866.92 N.
To determine the average net force, we can calculate acceleration using:
x = 0.5*a*t^2
v = a*t
where x=3.6m and v=185 m/s.
Thus,
t=v/a and therefore x = 0.5*a*(v/a)^2 = 0.5 * (v^2)/a
which gives us a= (0.5*v^2)/x
Since we have the known values of v and x, we can compute a by substituting these numbers.
The average net force is then given as:
F = m*a,
with m=7.5kg.
Explanation:
Data provided:
Area A = 10 cm×2 cm = 20×10⁻⁴ m²
Separation distance d between the plates = 1 mm = 1×10⁻³ m
Battery voltage, or emf = 100 V
Resistance = 1025 ohm
Solution:
In an RC circuit, the voltage across the plates varies with time t. At the outset, the voltage matches that of the battery, V₀ = emf = 100V. However, after a certain time t, both the resistance and capacitance alter this, leading to a final voltage V expressed as
Applying the natural logarithm to both sides,
(1)
Next, we can determine the capacitance using the plates' area.
C = ε₀A/d
= 
= 18×10⁻¹²F
We can now find the time it takes for the voltage to drop from 100 to 55 V by substituting C, V₀, V, and R values into equation (1)
= -(1025Ω)(18×10⁻¹² F) ln( 1 - 55/100)
= 15×10⁻⁹s
= 15 ns
Response:
(A) 4* 6 ^ ⁻6 T m² (B) 2 * 10 ^ ⁻6 v
Clarification:
Solution
Given that:
A refrigerator magnet with a depth of approximately 2 mm
The estimated magnetic field strength of the magnet is = 5 m T
The Area = 8 cm²
Now,
(A) The magnetic flux ΦB = BA
Therefore,
ΦB = (5 * 10^⁻ 3) ( 4 * 10 ^⁻2) * ( 2 * 10^ ⁻2) Tm²
Thus,
ΦB = 4* 6 ^ ⁻6 T m²
(B) By employing Faraday's Law, the subsequent equation applies:
Ε = Bℓυ
Where,
ℓ = 2 cm equals 2 * 10 ^⁻2 m
B = 5 m T = 5 * 10 ^ ⁻3 T
υ = 2 cm/s = 2 * 10 ^ ⁻2 m/s
Therefore,
Ε = (5 * 10 ^ ⁻3 T) * (2 * 10 ^ ⁻2) (2 * 10 ^ ⁻2) v
E =2 * 10 ^ ⁻6 v
Let T be the force exerted on the rope by her. This force induces tension in the rope, which exerts an upward force on the crates, while the weight of the crate pulls downward. Thus, the net force acting on the crate can be expressed as mg - T, acting in the downward direction. According to Newton's law, we can set up the equation: mg - T = ma. Given that a = 0 (the speed remains constant), this simplifies our equation to mg - T = 0, which leads to T = mg. Therefore, T = 25 x 9.8 = 245 N, indicating that the force she needs to apply is 245 N.
