Answer:
17.82J
Explanation:
Kinetic energy = 1/2 mv^2
Given
Mass M = 0.45kg
Velocity v = 8.9m/s
Therefore,
K.E. = 1/2 x 0.45 x (8.9)^2
= 1/2 x 0.45 x (8.9 x 8.9)
= 1/2 x 0.45 x 79.21
Multiply through
= 35.6445/2
= 17.82J
The kinetic energy of the ball is 17.82J
First question (upper left):
1/Req = 1/12 + 1/24 = 1/8
Req = 8 ohms
Voltage is equal through different resistors, and V1 = V2 = 24 V.
Current varies through parallel resistors: I1 = V1/R1 = 24/12 = 2 A. I2 = 24/24 = 1 A.
Second question (middle left):
V1 = V2 = 6 V (parallel circuits)
I1 = 2 A, I2 = 1 A, IT = 2+1 = 3 A.
R1 = V1/I1 = 6/2 = 3 ohms, R2 = 6/1 = 6 ohms, 1/Req = 1/2 + 1/1, Req = 2/3 ohms
Third question (bottom left):
V1 = V2 = 12 V
IT = 3 A, meaning Req = V/It = 12 V/3 A = 4 ohms
1/Req = 1/R1 + 1/R2, 1/4 = 1/12 + 1/R2, R2 = 6 ohms
I1 = V/R1 = 1 A, I2 = V/R2 = 2 A
Fourth question (top right):
1/Req = 1/20 + 1/20, Req = 10 ohms
IT = 4 A, so VT = IT(Req) = 4*10 = 40 V
Parallel circuits, so V1 = V2 = VT = 40 V
Since the resistors are identical, the current is split evenly between both: I1 = I2 = IT/2 = 2 A.
Fifth question (middle right):
1/Req = 1/5 + 1/20 + 1/4, Req = 2 ohms
IT = VT/Req = 40 V/2 ohms = 20 A
V1 = V2 = V3 = 40 V
The current of 20 A will be divided proportionally according to the resistances of 5, 20, and 4, the factors will be 5/(5+20+4), 20/(5+20+4), and 4/(5+20+4), which are 5/29, 20/29, and 4/29.
I1 = 20(5/29) = 100/29 A
I2 = 20(20/29) = 400/29 A
I3 = 20(4/29) = 80/29 A
Sixth question (bottom right):
V2 = 30V is given, but since these are parallel circuits, V1 = VT = 30 V.
Then I1 = V1/R1 = 30 V/10 ohms = 3 A.
I2 = 30 V/15 ohms = 2 A.
IT = 3 + 2 = 5 A
1/Req = 1/10 + 1/15, Req = 6 ohms
Answer:
The mass of the fluid is 72 g.
Explanation:
The following data were obtained from the question:
Height (h) = 10 cm
Area of cross section (A) = 36cm²
Relative density = 0.2
Mass =..?
Next, we shall determine the volume of the cylinder. This can be achieved by doing the following:
Volume = Area x Height
Volume = 36 x 10
Volume = 360 cm³
Next, we shall determine the density of the liquid.
This can be obtained as follow:
Relative density = density of substance/density of water.
Relative density = 0.2
Density of water = 1 g/cm³
Density of fluid =...?
Relative density = density of substance/density of water.
0.2 = density of fluid / 1 g/cm³
Cross multiply
Density of fluid = 0.2 x 1 g/cm³
Density of fluid = 0.2 g/cm³
Finally, we shall determine the mass of fluid as follow:
Volume = 360 cm³
Density of fluid = 0.2 g/cm³
Mass of fluid =...?
Density = mass /volume.
0.2 g/cm³ = mass of fluid /360 cm³
Cross multiply
Mass of fluid = 0.2 g/cm³ x 360 cm³
Mass of fluid = 72 g
Therefore, the mass of the fluid in the jar is 72 g.
