Answer:A uniform ladder of mass and length leans at an angle against a frictionless wall .If the coefficient of static friction between the ladder and the ground is , determine a formula for the minimum angle at which the ladder will not slip.
Explanation:A uniform ladder of mass and length leans at an angle against a frictionless wall .If the coefficient of static friction between the ladder and the ground is , determine a formula for the minimum angle at which the ladder will not slip.
Answer:
a) v² = G M R³, b) T = 2π /
, c) 
Explanation:
a) The kinetic energy is
K = ½ m v²
to find the velocity let's use Newton's second law
F = m a
acceleration is centripetal
a = v² / R
force is the universal force of attraction
F = G m M / r²
we substitute
G m M R² = m v² R
v² = G M R³
the kinetic energy is
K = ½ m G M R³
b) angular and linear velocity are related
v = w R
w = v / R
w =
w =
the angular velocity is related to the period
w = 2π / T
T = 2π / w
we substitute
T = 2π /
c) the angular moeomto is
L = m v r
L = m RA G M R³ R
L = 
Kinetic energy = (1/2) (mass) (speed)²
Since the 'speed' in the KE formula is squared, if the car's speed
increases by 5 times, its kinetic energy increases by (5²) = 25 times.
The loss of kinetic energy in a skid is just the wo0rk done by friction
between the tires and pavement. So the skid distance is proportional
to the initial kinetic energy, and the car must skid 25 times as far when
it enters the skid at the higher speed.
25 x 30m = 750 meters
Given:
ρ = 1.18 kg/m³, density of air
v = 8 m/s, flow velocity
Q = 9 m³/s, volumetric flow rate
The minimum power required (at 100% efficiency) is

The actual power will be higher because 100% efficiency is not possible.
Answer: 339.8 W (nearest tenth)