Answer:
250Nm
Explanation:
Given parameters:
Length of the long pry bar = 1m
Force acting on it = 250N
Angle = 90°
Unknown:
Amount of torque applied = ?
Solution:
Torque is the turning force on a body that causes the rotation of the body.
The formula is given as:
Torque = Force x r Sin Ф
r is the distance
So;
Torque = 250 x 1 x sin 90 = 250Nm
The kinetic energy with which the hammer strikes the ground
is exactly the potential energy it had at the height from which it fell.
Potential energy is (mass) x (gravity) x (height) .... directly proportional
to height.
Starting from double the height, it starts with double the potential
energy, and it reaches the bottom with double the kinetic energy.
Answer:
w = √[g /L (½ r²/L2 + 2/3 ) ]
When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE
Explanation:
We can simulate this system as a physical pendulum, which is a pendulum with a distributed mass, in this case the angular velocity is
w² = mg d / I
In this case, the distance d to the pivot point of half the length (L) of the cylinder, which we consider long and narrow
d = L / 2
The moment of inertia of a cylinder with respect to an axis at the end we can use the parallel axes theorem, it is approximately equal to that of a long bar plus the moment of inertia of the center of mass of the cylinder, this is tabulated
I = ¼ m r2 + ⅓ m L2
I = m (¼ r2 + ⅓ L2)
now let's use the concept of density to calculate the mass of the system
ρ = m / V
m = ρ V
the volume of a cylinder is
V = π r² L
m = ρ π r² L
let's substitute
w² = m g (L / 2) / m (¼ r² + ⅓ L²)
w² = g L / (½ r² + 2/3 L²)
L >> r
w = √[g /L (½ r²/L2 + 2/3 ) ]
When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE
Explanation:
We have,
Semimajor axis is 
It is required to find the orbital period of a dwarf planet. Let T is time period. The relation between the time period and the semi major axis is given by Kepler's third law. Its mathematical form is given by :
G is universal gravitational constant
M is solar mass
Plugging all the values,
Since,
So, the orbital period of a dwarf planet is 138.52 years.
