Answer:
Explanation:
Let T be the tension .
Applying newton's second law on the downward movement of the bucket
mg - T = ma
On the drum , a torque of TR will be acting which will create an angular acceleration of α in it . If I be the moment of inertia of the drum
TR = Iα
TR = Ia/ R
T = Ia/ R²
Replacing this value of T in the other equation
mg - T = ma
mg - Ia/ R² = ma
mg = Ia/ R² +ma
a ( I/ R² +m)= mg
a = mg / ( I/ R² +m)
mg - T = ma
mg - ma = T
mg - m x mg / ( I/ R² +m) = T
mg - m²g / ( I/ R² +m ) = T
mg - mg / ( 1 + I / m R² ) = T
b ) T = Ia/ R²
I = TR² / a
c ) Moment of inertia of hollow cylinder
I = 1/2 M ( R² - R² / 4 )
= 3/4 x 1/2 MR²
= 3/8 MR²
I / R² = 3/8 M
a = mg / ( I/ R² +m)
a = mg / ( 3/8 M + m )
T = Ia/ R²
= 3/8 MR² x mg / ( 3/8 M + m ) x 1 /R²
= 
Answer:
C) 40 N/m
Explanation:
If we ASSUME that the spring is un-stretched at the zero cm position
k = F/Δx = 10/0.25 = 40 N/m
Answer:
Explanation:
Power is defined as the energy produced (E) per unit of time (t):
This means that the energy produced in the Sun each second (1 s), given the power 
, is
Each p-p chain reaction produces an amount of energy of
in order to get the total number of p-p chain reactions per second, we need to divide the total energy produced per second by the energy produced by each reaction:
Answer: a) vcar= 7 m/s ; b) a train= 0.65 m/s^2
Explanation: By using the kinematic equation for the car and the train we can determine the above values of the car velocity and the acceletarion of the train, respectively.
We have for the car
distance = v car* t, considering the length of train (81.1 m) travel by the car during the first 11.6 s
the v car = distance/time= 81.1 m/11.6s= 7 m/s
In order to calculate the acceleration we have to use the kinematic equation for the train from the rest
distance train = (a* t^2)/2
distance train : distance travel by the car at constant speed
so distance train= (vcar*36.35)m=421 m
the a traiin= (2* 421 m)/(36s)^2=0.65 m/s^2
Answer:
W = 1,307 10⁶ J
Explanation:
Work is the product of force by distance, in this case it is the force of gravitational attraction between the moon (M) and the capsule (m₁)
F = G m₁ M / r²
W = ∫ F. dr
W = G m₁ M ∫ dr / r²
we integrate
W = G m₁ M (-1 / r)
We evaluate between the limits, lower r = R_ Moon and r = ∞
W = -G m₁ M (1 /∞ - 1 / R_moon)
W = G m1 M / r_moon
Body weight is
W = mg
m = W / g
The mass is constant, so we can find it with the initial data
For the capsule
m = 1000/32 = 165 / g_moon
g_moom = 165 32/1000
.g_moon = 5.28 ft / s²
I think it is easier to follow the exercise in SI system
W_capsule = 1000 pound (1 kg / 2.20 pounds)
W_capsule = 454 N
W = m_capsule g
m_capsule = W / g
m = 454 /9.8
m_capsule = 46,327 kg
Let's calculate
W = 6.67 10⁻¹¹ 46,327 7.36 10²² / 1.74 10⁶
W = 1,307 10⁶ J
