Answer:
angle minimum θ = 41.3º
Explanation:
For this exercise let's use Newton's second law in the condition of static equilibrium
N - W = 0
N = W
The rotational equilibrium condition, where we place the axis of rotation on the wall
We assume that counterclockwise rotations are positive
fr (l sin θ) - N (l cos θ) + W (l/2 cos θ) = 0
the friction force formula is
fr = μ N
fr = μ W
we substitute
μ m g l sin θ - m g l cos θ + mg l /2 cos θ = 0
μ sin θ - cos θ + ½ cos θ= 0
μ sin θ - ½ cos θ = 0
sin θ / cos θ = 1/2 μ
tan θ = 1/2 μ
θ = tan⁻¹ (1 / 2μ)
θ = tan⁻¹ (1 (2 0.57))
θ = 41.3º
When white light passes through a prism, violet is the color that is refracted the most.
Answer:
Explanation:
Displacement involves direction and distance. In this case, the deer has walked a distance of 17 + 12 = 29m but because of the South-then-North direction, the net displacement is only 17-12 = 5m.
So the answer is A) 5.0 m, 29.0 m
Answer:
-2.869 rad/s2
Explanation:
Data given:
speed, vi at 95.0 km/h = 95 X (1 hour /3600 seconds) X (1000m / 1km)
Note that, for every 1 hour, there will be 60sec X 60sec = 3600 seconds
And for every 1km, there will be 1000m.
So, speed of 95.0 km/h = 26.389 m/s
speed, vi = r
ω (radius X angular velocity)
angular velocity, ωi = v/r
ωi = 26.389 m/s ÷ half of 0.88 m diameter
= 59.975 rad/s
decelerating to speed, vf at 60.0 km/h = 60 X X (1 hour /3600 seconds) X (1000m / 1km)
= 16.667m/s
The angular velocity for this speed = 16.667m/s ÷ half of 0.88 m diameter
= 37.879rad/s
How far the car goes is equivalent to the angular acceleration which equals to (ωf^2 - ωi^2) ÷ 2θ
= (37.879rad/s)^2 - (59.975 rad/s)^2 ÷ 2 (60 rev X 2π rad/rev)
= -2.869 rad/s2
Answer:
1. Wavelength = 3.2 m
2. Amplitude = 0.6 m
Explanation:
1. Determination of the wavelength.
The wavelength of a wave is defined as the distance between two successive crest. This implies that for every complete vibration, there is one wavelength.
From the diagram given above, we can see that the wave makes 2½ vibrations.
This means that there are 2½ equal wavelength of the wave. Therefore, the wavelength can be obtained as follow:
Length (L) = 8 m
Wavelength (λ) =?
2½ λ = L
5/2 λ = 8
5λ / 2 = 8
Cross multiply
5λ = 2 × 8
5λ = 16
Divide both side by 5
λ = 16 / 5
λ = 3.2 m
Therefore, wavelength of the wave is 3.2 m.
2. Determination of the amplitude.
The amplitude of a wave is defined as the maximum displacement of the wave from the origin.
From the diagram given above, the distance between the maximum and minimum displacement is given as 1.2 m. Thus, we can obtain the amplitude of wave as follow:
Distance between the maximum and minimum displacement (D) = 1.2
Amplitude (A) =?
A = ½D
A = ½ × 1.2
A = 0.6 m
Thus, the amplitude of the wave is 0.6 m
