Projectile motion range is the horizontal distance traveled. Stable equilibrium, seen in a balanced seesaw, contrasts with unstable equilibrium, as in an inverted pendulum. The least pressure the box can exert on a horizontal surface is 8000 Pa. For floating, Buoyant Force must surpass weight, and object density must be less than liquid density. Equilibrium arises when buoyancy equals gravity.
The maximum range of a projectile motion is the horizontal distance traveled by the projectile. An example of an object in stable equilibrium is a balanced seesaw, while an inverted pendulum represents unstable equilibrium due to its precarious position.
To calculate the pressure exerted by the box on a horizontal surface, you can use the formula:
Pressure = Force / Area
The force here is the weight of the box (Force = Weight), and the area is the contact area of the box with the surface.
Calculate the weight of the box:
Weight = mass * gravity
Weight = 60 kg * 10 m/s^2
Weight = 600 N
Calculate the contact area:
Area = length * width
Area = 0.25 m * 0.3 m
Area = 0.075 m^2
Calculate the pressure:
Pressure = 600 N / 0.075 m^2
Pressure = 8000 Pa
So, the least pressure the box can exert on a horizontal surface is 8000 Pa.
As for the conditions for a body to float on a liquid, there are two main factors:
Buoyant Force: For an object to float, the buoyant force (upward force exerted by a fluid on an immersed object) must be greater than or equal to the weight of the object. Mathematically, this is expressed as:
Buoyant Force ≥ Weight of the Object
Density: The average density of the object must be less than the density of the liquid. Mathematically, this is expressed as:
Density of the Object < Density of the Liquid
If these conditions are met, the object will float on the liquid.
A floating object in equilibrium experiences two main forces: buoyancy and gravity. Buoyancy, an upward force exerted by a fluid (liquid or gas), counteracts the object's weight. It is equal to the weight of the fluid displaced by the object.
Gravity, acting downward, represents the object's weight. When an object is at rest in a fluid, these forces balance, creating equilibrium.