The cart is at rest, so it is in equilibrium and there is no net force acting on it. The only forces acting on the cart are its weight (magnitude <em>w</em>), the normal force (mag. <em>n</em>), and the friction force (maximum mag. <em>f</em> ).
In the horizontal direction, we have
<em>n</em> cos(120º) + <em>f</em> cos(30º) = 0
-1/2 <em>n</em> + √3/2 <em>f</em> = 0
<em>n</em> = √3 <em>f</em>
and in the vertical,
<em>n</em> sin(120º) + <em>f</em> sin(30º) + (-<em>w</em>) = 0
<em>n</em> sin(120º) + <em>f</em> sin(30º) = (50 kg) (9.80 m/s²)
√3/2 <em>n</em> + 1/2 <em>f</em> = 490 N
Substitute <em>n</em> = √3 <em>f</em> and solve for <em>f</em> :
√3/2 (√3 <em>f </em>) + 1/2 <em>f</em> = 490 N
2 <em>f</em> = 490 N
<em>f</em> = 245 N
(pointed up the incline)
Answer:
The angular velocity is 15.37 rad/s
Solution:
As per the question:

Horizontal distance, x = 30.1 m
Distance of the ball from the rotation axis is its radius, R = 1.15 m
Now,
To calculate the angular velocity:
Linear velocity, v = 
v = 
v = 
v = 
Now,
The angular velocity can be calculated as:

Thus

Answer:
841.5 Hz
Explanation:
Given
y = 50 cm = 0.5 m
d = 5.00 m
L = 12.0 m away from the wall
v = speed of sound = 343 m/s
The image of the scenario is presented in the attached image.
When destructive interference is being experienced from 50 cm (0.5 m) parallel to the wall, the path difference between the distance of the two speakers from the observer is equal to half of the wavelength of the wave.
Let the distance from speaker one to the observer's new position be d₁
And the distance from the speaker two to the observer's new position be d₂
(λ/2) = |d₁ - d₂|
d₁ = √(12² + 3²) = 12.3693 m
d₂ = √(12² + 2²) = 12.1655 m
|d₁ - d₂| = 0.2038 m
(λ/2) = |d₁ - d₂| = 0.2038
λ = 0.4076 m
For waves, the velocity (v), frequency (f) and wavelength (λ) are related thus
v = fλ
f = (v/λ) = (343/0.4076) = 841.5 Hz
Hope this Helps!!!
Answer:
7.1 m/s
Explanation:
First, find the time it takes for the fish to reach the water.
Given in the y direction:
Δy = 6.1 m
v₀ = 0 m/s
a = 9.8 m/s²
Find: t
Δy = v₀ t + ½ at²
6.1 m = (0 m/s) t + ½ (9.8 m/s²) t²
t = 1.12 s
Next, find the velocity needed to travel 7.9 m in that time.
Given in the x direction:
Δx = 7.9 m
a = 0 m/s²
t = 1.12 s
Find: v₀
Δx = v₀ t + ½ at²
7.9 m = v₀ (1.12 s) + ½ (0 m/s²) (1.12 s)²
v₀ = 7.1 m/s