-GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.
Given
A particle of mass m moving under the influence of a fixed mass's M, gravitational potential energy of formula -GMm/r, where r is the separation between the masses and G is the gravitational constant of the universe.
As the Gravity Potential energy of particle = -GMm/r
Total energy of particle = Kinetic energy + Potential Energy
As we know that
Kinetic energy = 1/2mv²
Also, v is equals to square root of GM/r
v = √GM/r
Put the value of v in the formula of kinetic energy
We get,
Kinetic Energy = GMm/2r
Total Energy = GMm/2r + (-GMm/r)
= GMm/2r - GMm/r
= -GMm/2r
Hence, -GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.
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The heat energy released from a piece of wire or any other section of a circuit is:
Energy = (voltage between its ends) x (current through it) x (time it's been going)
Answer:
The final velocity of the ball is 39.2 m/s.
Explanation:
Given that,
A ball is dropped from rest from a high window of a tall building.
Time = 4 sec
We need to calculate the final velocity of the ball
Using equation if motion

Where, v = final velocity
u = initial velocity
g = acceleration due to gravity
t = time
Put the value into the formula


Hence, The final velocity of the ball is 39.2 m/s.
Answer:
4.535 N.m
Explanation:
To solve this question, we're going to use the formula for moment of inertia
I = mL²/12
Where
I = moment of inertia
m = mass of the ladder, 7.98 kg
L = length of the ladder, 4.15 m
On solving we have
I = 7.98 * (4.15)² / 12
I = (7.98 * 17.2225) / 12
I = 137.44 / 12
I = 11.45 kg·m²
That is the moment of inertia about the center.
Using this moment of inertia, we multiply it by the angular acceleration to get the needed torque. So that
τ = 11.453 kg·m² * 0.395 rad/s²
τ = 4.535 N·m
Answer:
The speed of the resistive force is 42.426 m/s
Explanation:
Given;
mass of skydiver, m = 75 kg
terminal velocity, 
The resistive force on the skydiver is known as drag force.
Drag force is directly proportional to square of terminal velocity.

Where;
k is a constant

When the new drag force is half of the original drag force;

Therefore, the speed of the resistive force is 42.426 m/s