Answer:
d=1.07m
Explanation:
Calculate Initial Kinetic Energy:
KE = 1/2*m*v^2
KE= 0.5*(10.3kg)*(1.64m/s)^2 = 13.85J
Calculate work overcoming friction:
W = F*d = mu*m*g*d
W = (0.128)*(10.3kg)*9.80m/s^2)*d
W = 12.92*d
Equate the two since all of the kinetic energy is used up in working against friction:
W = KE
12.92d = 13.851J
Solve for d:
d= (13.851J)/(12.92) = 1.07 m
To solve this problem it is necessary to apply the concepts related to the condition of path difference for destructive interference between the two reflected waves from the top and bottom of a surface.
Mathematically this expression can be described under the equation

Where
n = Refractive index
t = Thickness
In terms of the wavelength the path difference of the reflected waves can be described as

Where
\lambda = Wavelenght
Equation the two equations we have that


Our values are given as
Wavelength of light



Therefore the minimum thickness of the oil for destructive interference to occur is approximately 34.0 nm
Answer:
the runner's average kinetic energy during the run is 476.96 J.
Explanation:
Given;
mass of the runner, m = 85 kg
distance covered by the runner, d = 42.2 km = 42,200 m
time to complete the race, t = 3 hours 30 mins = (3 x 3600s) + (30 x 60s)
= 12,600 s
The speed of the runner, v = d/t
v = 42,200 / 12,600
v = 3.35 m/s
The runner's average kinetic energy during the run is calculated as;
K.E = ¹/₂mv²
K.E = ¹/₂ × 85 × (3.35)²
K.E = 476.96 J
Therefore, the runner's average kinetic energy during the run is 476.96 J.
Answer:
When the temperature of the coffee is 50 °C, the time will be 20.68 mins
Explanation:
Given;
The initial temperature of the coffee T₀ = 95 °C
The temperature of the room = 21°C
Let T be the temperature at time of cooling t in mins
According to Newton's law of cooling;

When the temperature is 50 °C, the time t in min is calculated as;

Therefore, when the temperature of the coffee is 50 °C, the time will be 20.68 mins