A beaker of water placed on a scale produces a reading of 0.910kg. An object of mass 0.27kg and volume 9.40 x 10^-5m^3 is lowered into the water by a string. By how much will the reading on scale change?
first check the density of this object.
.27 kg/.000094 m^3 = 2872 kg/m^3
water density is 1000 so this thing sinks.
The tension in the string will decrease by the volume of the object * density of water * g
= .000094 * 1000 g = .094 g Newtons
the water pushes up with .094 g so the scale has to push up with an additional .094 g N
since our scale is calibrated for mass on earth in kg it will read an additional .094 kg
To determine how the reading on the scale will change when the object is lowered into the water, we need to consider the buoyant force acting on the object.
The buoyant force is equal to the weight of the water displaced by the object. So, we first need to calculate the weight of the water displaced by the object.
Given:
Mass of the object, m = 0.27 kg
Volume of the object, V = 9.40 x 10^-5 m^3
Density of water, ρ = 1000 kg/m^3 (approximately)
The weight of the water displaced can be calculated using the formula:
Weight of water = Volume of water displaced × Density of water
Since the volume of water displaced is equal to the volume of the object, we have:
Weight of water = V × ρ
Now, let's calculate the weight of the water displaced:
Weight of water = (9.40 x 10^-5 m^3) × (1000 kg/m^3)
Weight of water = 0.0940 kg
The buoyant force acting on the object is equal to the weight of the water displaced, which in this case is 0.0940 kg.
Since the scale measures the force exerted on it, the reading on the scale will change by the same amount as the buoyant force. Therefore, the reading on the scale will change by 0.0940 kg.
To determine how much the reading on the scale will change, we need to calculate the change in weight caused by the object submerged in water.
Step 1: Calculate the weight of the water in the beaker.
The weight of the water is equal to the mass of the water multiplied by the acceleration due to gravity.
Given:
Mass of water = 0.910 kg
Acceleration due to gravity = 9.8 m/s^2
Weight of water = mass of water x acceleration due to gravity
Weight of water = 0.910 kg x 9.8 m/s^2
Weight of water = 8.918 N
Step 2: Calculate the buoyant force exerted on the object.
The buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Given:
Density of water = 1000 kg/m^3 (approximate value for water)
Volume of the object = 9.40 x 10^-5 m^3
Weight of the object = mass of the object x acceleration due to gravity
Weight of the object = 0.27 kg x 9.8 m/s^2
Weight of the object = 2.646 N
Buoyant force = weight of fluid displaced by the object
Buoyant force = density of fluid x volume of object x acceleration due to gravity
Buoyant force = 1000 kg/m^3 x (9.40 x 10^-5 m^3) x 9.8 m/s^2
Buoyant force = 0.09212 N
Step 3: Calculate the change in weight on the scale.
The change in weight is equal to the buoyant force exerted on the object.
Change in weight = Buoyant force
Change in weight = 0.09212 N
Therefore, the reading on the scale will change by approximately 0.09212 Newtons.