Answer:(a) 4775.2Hz (b) 4.06m/s (c) 19382.15m/s²
Explanation: Given that the frequency of oscilation f, is 760Hz and the maximum displacement x, is 0.85mm= 0.00085m
(a) Angular frequency w= 2πf
w= 2π × 760 = 4775.2Hz
(b) Maximum speed v is given as the product of angular frequency and maximum displacement
V=wx
V= 4775.2 × 0.00085
V= 4.06m/s
(c) The maximum acceleration a
= w²x
= (4775.2)² × (0.00085)
a= 19382.15m/s².
Answer:
A) the maximum acceleration the boulder can have and still get out of the quarry
B) how long does it take to be lifted out at maximum acceleration if it started from rest
Explanation:
A)
let +y is upward. look below at the free body diagram. the mass M refers to the combined mass of the boulder and chain.
the weight of the chain is:
and maximum tension is 
total mass and weight is :


∑



B)
maximum acceleration

using 
to solve for t


Assume the snow is uniform, and horizontal.
Given:
coefficient of kinetic friction = 0.10 = muK
weight of sled = 48 N
weight of rider = 660 N
normal force on of sled with rider = 48+660 N = 708 N = N
Force required to maintain a uniform speed
= coefficient of kinetic friction * normal force
= muK * N
= 0.10 * 708 N
=70.8 N
Note: it takes more than 70.8 N to start the sled in motion, because static friction is in general greater than kinetic friction.
1)
p = 2.4 * 10^5 Pa
T = 18° C + 273.15 = 291.15 k
r = 0.25 m => V = [4/3]π(r^3) = [4/3]π(0.25m)^3 = 0.06545 m^3 = 65.45 L
Use ideal gas equation: pV = nRT => n = pV / RT = [2.4*10^5 Pa * 0.06545 m^3] / [8.31 J/k*mol * 291.15k] = 6.492 mol
Avogadro number = 1 mol = 6.022 * 10^23 atoms
Number of atoms = 6.492 mol * 6.022 *10^23 atom/mol = 39.097 * 10^23 atoms = 3.91 * 10^24 atoms
2) Double atoms => double volume
V2 / V1 = r2 ^3 / r1/3
2 = r2 ^3 / r1 ^3 => r2 ^3 = 2* r1 ^3
r2 = [∛2]r1
The factor is ∛2
True. Think of a magnet and how they only connect to the opposite charges.