The equilibrium conditions allow to find the results for the balance forces are:
When the acceleration is zero we have the equilibrium conditions for both linear and rotational motion.
∑ F = 0
∑ τ = 0
Where F are the forces and τ the torques.
The torque is the product of the force and the perpendicular distance to the point of support,
The free-body diagrams are diagrams of the forces without the details of the bodies, see attached for the free-body diagram of the system.
We write the translational equilibrium condition.
F₁ - W₁ - W₂ + F₂ = 0
We write the equation for the rotational motion, set our point of origin at scale 1, and the counterclockwise turns are positive.
F₂ 2 - W₁ 1 - W₂ 1.5 = 0
Let's calculate F₂
F₂ = 
F₂ = (m g + M g 1.5)/ 2
F₂ = 
F₂ = 558.6 N
We substitute in the translational equilibrium equation.
F₁ = W₁ + W₂ - F₂
F₁ = (m + M) g - F₂
F₁ = (12 +68) 9.8 - 558.6
F₁ = 225.4 N
In conclusion using the equilibrium conditions we can find the forces of the balance are:
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The leaf fell at the crooked path instead of straight down because air currents and gravity applied changing and unbalanced forces to the leaf.
<h3>What is an air current?</h3>
An air current is defined as the changes in atmospheric pressure that causes the movement of air from one area to another.
When a leaf is detached naturally from the tree, it won't fall straight down to the floor but will fall a distance away from the tree due to the action of air current and some unbalanced forces.
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Vi = 15 m/s
t = 2 s
a = 9.8 m/s^2
y = ?
The kinematic equation that has all of our variables is d = Vi*t + 0.5*a*t^2
y = 15*2 + 0.5*9.8*2^2 = 49.6 m
Jemima is running with a velocity of 5m/s. She has a mass of 65kg, what is her kinetic energy would be 812.5 Joules.
<h3>What is mechanical energy?</h3>
Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.
As given in the problem we have to calculate the Kinetic energy of the Jemima,
Kinetic energy = 1/2 ×mass×velocity²
=0.5×65×5²
=812.5 Joules
Thus, the kinetic energy of the Jemima would be 812.5 Joules.
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