Answer:
v = (5.2 ± 0.2) 10⁻² m / s
Explanation:
This is an exercise in kinematics of uniform motion. The formula for the average speed is
v = x / t
let's calculate
v = 5.2 / 100
v = 0.052 m / s
v = 5.2 10-2 m / s
we have to find the uncertainty of this quantity we propagate the error using derivatives
Δv = dv /dx Δx + dv /dt Δt
taking everything in the most unfavorable case, I mean all positive
let's make the derivatives
dv / dx = 1 / t
dv / dt = -x / t²
we substitute
Δv = 1 /t Δx + x /t² Δt
let's calculate the error
Δv = 1/100 0.1 + 5.2 / 100² 1
Δv = 1 10⁻³ + 5.2 10⁻⁴
Δv = 1.52 10⁻³ m/s
the error must be given with a significant figure
Dv = 2 10⁻³ m / s
the answer is
v = (5.2 ± 0.2) 10⁻² m / s
Boundary separating two masses of air of different densities
Answer:
tension far end 883.055714 N
tension closer 578.634286 N
Explanation:
Given data
scaffold mass m1 = 64 kg
scaffold length L1 = 6.3 m
window washer mass m2 = 85 kg
distance L2 = 2 m
to find out
tension near cable and farther cable
solution
torques at the end farthest
(m1 × g × L1 ) / 2 + (m2 × g × L1- L2 ) = T × L1
T × 6.3 = (64 × 9.81 × 6.3 ) / 2 + (85 × 9.81 × 4.3 )
T = 5563.251 / 6.3
tension = 883.055714 N
and
torques at the other end,
(m1 × g × L1 ) / 2 + (m2 × g × L2 ) = T × L1
T × 6.3 = (64 × 9.81 × 6.3 ) / 2 + (85 × 9.81 × 2 )
T = 3645.396 / 6.3
tension = 578.634286 N
Answer:
a)
85.05 N/m
b)
179.81 rad/s
Explanation:
a)
k = spring constant of the spring
m = mass of the block = 0.473 kg
x = stretch caused in the spring = 0.109 m
h = height dropped by the block = 0.109 m
Using conservation of energy
Spring potential energy gained by the spring = Potential energy lost by the block
(0.5) k x² = mgh
(0.5) k x² = mgx
(0.5) k x = mg
(0.5) k (0.109) = (0.473) (9.8)
k = 85.05 N/m
b)
angular frequency is given as
= 179.81 rad/s
A. Is very attractive. If it's sublimation directly from water vapor in the air to ice on the glass, then yes. But from liquid water mist to water ice, no. Ice is less dense than water. That's why cubes float in your soda. Better leave 'A' alone. . . . D. Ice pellets turn to liquid. That one's good.