Answer:
f = 3.09 Hz
Explanation:
This is a simple harmonic motion exercise where the angular velocity is
w² = 
to find the constant (k) of the spring, we use Hooke's law with the initial data
F = - kx
where the force is the weight of the body that is hanging
F = W = m g
we substitute
m g = - k x
k = 
we calculate
k = 
k = 3.769 10² m
we substitute in the first equation
w² = 
w = 19.415 rad / s
angular velocity and frequency are related
w = 2πf
f = 
f = 19.415 / 2pi
f = 3.09 Hz
Answer:
Volume = 1,015 acre-feet (Approx)
Explanation:
Given:
Rain = 1.7 in
Time = 30 min
Area = 29 km²
Find:
Volume in acre-feet
Computation:
1 km = 1,000 m
1 m = 3.28 feet
1 km² = 247.105 acre
d = 1.7 in = 1.7 / 12 = 0.14167 ft
Area = 29 × 247.105 = 7,166.045 acre
Volume = 7,166.045 acre × 0.14167 ft
Volume = 1,015 acre-feet (Approx)
Answer:
Explanation:
From the given information:
the car's momentum = momentum of the truck
∴
(a) 816 kg × v = 2650 kg × 16.0 km/h
v = (2650 kg × 16.0 km/h) / 816 kg
v = 51.96 km/hr
(b) 816 kg × v = 9080 kg × 16.0 km/h
v = (9080 kg × 16.0 km/h) / 816 kg
v = 178.04 km/hr
The text does not specify whether the resistance R of the wire must be kept the same or not: here I assume R must be kept the same.
The relationship between the resistance and the resistivity of a wire is
where
is the resistivity
A is the cross-sectional area
R is the resistance
L is the wire length
the cross-sectional area is given by
where r is the radius of the wire. Substituting in the previous equation ,we find
For the new wire, the length L is kept the same (L'=L) while the radius is doubled (r'=2r), so the new resistivity is
Therefore, the new resistivity must be 4 times the original one.
Remember Newton's second law: F=ma
to get the force in newtons, mass should be in kg and acceleration in m/s^2
conveniently, we don't need to convert units
we just need to multiply the two to get the force
65* 0.3 = 19.5 kg m/s^2 or N
if significant digit is an issue, the least number if sig figs is 1 so the answer would be 20 N
