Answer:
<h2>
d₂ = 3d</h2><h2>
The diameter of the second wire is 3 times that of the initial wire.</h2>
Explanation:
Using the formula for calculating the resistivity of an object to find the diameter.
Resistivity P = RA/L
R is the resistance of the material
A is the cross sectional area
L is the length of the material
Since A = πd²/4
P = R( πd²/4)/L
P = Rπd²/4L ... 1
If the second wire of the same material and length is found to have resistance R/9, the resistivity of the second material will be;
P₂ = (R/9)A₂/L₂
P₂ = (R/9)(πd₂²/4)/L₂
P₂ = (Rπd₂²/36)/L₂
P₂ = (Rπd₂²)/36L₂
Since the length and resistivity are the same;
P = P₂ and L =L₂
Equating 1 and 2;
Rπd²/4L = (Rπd₂²)/36L₂
Rπd²/4L = (Rπd₂²)/36L
d² = d₂²/9
d₂² = 9d²
Taking the square root of both sides;
√d₂² = √9d²
d₂ = 3d
Therefore the diameter of the second wire is 3 times that of the initial wire
Answer:
A. potential energy is 258720 Joule
Explanation:
A.Gravitational potential energy is: PE = m × g × h
velocity = 15.33 m/s when the car reaches the bottom of the hill.
where, m = mass
g = acceleration due to gravity
h = height from the bottom of hill.
The potential energy is : m×g×h
=(2200×9.8×12)
=258720 Joule
B. at the bottom of the hill, the potential energy is converted into kinetic energy so PE at top = KE at bottom
kinetic energy= ()
where v = velocity
m= mass
therefore, v=
or, v=
or, v=15.33 m/s
Answer:
See the answer below
Explanation:
1. Speed is calculated as the ratio of distance and time. Hence, Jame's speed can be calculated as:
400/5 km/hr = 80 km/hr
The unit for the speed would be km/hr. This can also be converted to m/s:
80 km = 80,000 m
1 hr = 3,600 s
80 km/hr = 80,000/3600 m/s = 22.22 m/s
2. Since James drove 400 km in 5 hours, the distance he drove is 400 km.
3. The time it took for James to get there is 5 hours.
Answer:
The distance the log has moved by the time Ernie reaches Bur is 1.33 m.
Explanation:
give information:
The log is 3.0 m long and has mass 20.0 kg.
Burt has mass 30.0 kg; Ernie has mass 40.0 kg
Ernie has mass 40.0 kg.
to find the distance, first, we have to calculate the center of mass
X = ∑ m x /∑m
= (20 x (3/2)) + (30 x 0) + (40 x 3)/ (20+30+40)
= 150/90
= 5/3
when Ernie walk, the center of the mass is
X = (70 x 0) + (20 x (3/2))/(70 + 20)
= 30/90
= 1/3
the distance of log moved = 5/3 - 4/3 = 1.33 m
Answer:
Explanation:
The rod will act as pendulum for small oscillation .
Time period of oscillation
angular frequency ω = 2π / T
=
b )
ω = 20( given )
velocity = ω r = ω l
Let the maximum angular displacement in terms of degree be θ .
1/2 m v ² = mgl ( 1 - cosθ ) ,
[ l-lcosθ is loss of height . we have applied law of conservation of mechanical energy .]
.5 ( ω l )² = gl( 1 - cos θ )
.5 ω² l = g ( 1 - cosθ )
1 - cosθ = .5 ω² l /g
cosθ = 1 - .5 ω² l /g
θ can be calculated , if value of l is given .