Answer:
T = mg - (m²g/(I/R² + m))
Explanation:
Let T be the tension in the cable between the drum and the bucket
Now, by applying newton's second law of gravity on the downward movement of the bucket, we will obtain;
mg - T = ma - - - - (eq1)
Now, on the drum , a torque of TR will be acting which will create an angular acceleration of "α" in it.
Where R is the radius.
Let "I" denote the moment of inertia of the drum. Thus, we have;
TR = Iα
Now, the angular acceleration is expressed in the form;
α = a/R
Where a is the linear downward acceleration.
Thus;
TR = Ia/ R
T = Ia/ R²
Let's put Ia/ R² for T into equation 1 to give;
mg - Ia/R² = ma
Ia/R² + ma = mg
a( I/R² + m) = mg
a = mg/(I/R² +m)
Now putting mg/(I/R² +m) for a in eq 1 gives;
mg - T = m(mg/(I/R² +m))
T = mg - m(mg/(I/R² +m))
T = mg - m²g/(I/R² + m)
Answer: 3.53 x 10^-4 s
Explanation:
12.7cm x 1m/100cm = 0.127m
V = d/t
t x V = d
t = d/v = 0.127m/(360m/s) = 0.000353s or 3.53 x 10^-4
Answer:
The sketch for the Gravitational force F and the potential energy U are attached to this answer.
Explanation:
To obtain the gravitational force, we can consider the gravitational field GF(r) as:
To calculate the gravitational field we can use the Gauss theorem. By considering a homogeneous mass of the sphere (constant density) and the spherical symmetry, we can determinate than the gravitational field direction is .
Considering a constant density:
Applying a spherical gaussian surface for different radius r:
for R<b:
for b<R<a:
for a<R:
For the potential energy you can integrate the field to obtain the gravitational potential and the multiplying for the particle mass:
for a<R:
for b≤R≤a:
for R≤b:
Within the elastic limit of a solid material, the deformation (strain) produced by a force (stress) of any kind is proportional to the force. If the elastic limit is not exceeded, the material returns to it original shape and size after the force is removed, other it remains deformed or stretched.