PHYSM-(c) Fig. 1.2 shows the cylinder immersed in

Sure, let's address the questions based on the provided images and information. Question 1: Calculate the density of the liquid

Solution

a

Use the pressure formula for a fluid column:

P = \rho g h

b

Rearrange the formula to solve for density:

\rho = \frac{P}{g h}

c

Substitute the given values:

P = 560 \, \text{Pa}, \, g = 9.8 \, \text{m/s}^2, \, h = 2.7 \, \text{cm} = 0.027 \, \text{m}

d

Calculate the density:

\rho = \frac{560}{9.8 \times 0.027} \approx 2130 \, \text{kg/m}^3

Answer

2130 kg/m³

Key Concept

Pressure in a fluid column:

P = \rho g h

Explanation

The pressure at a certain depth in a fluid is given by the product of the fluid's density, gravitational acceleration, and the depth. By rearranging the formula, we can solve for the density.

Question 2: Explain why the cylinder does not float in this liquid

Solution

a

Apply Archimedes' Principle: The buoyant force is equal to the weight of the displaced liquid

b

For the cylinder to float, the buoyant force must be equal to the weight of the cylinder

c

Since the cylinder does not float, the weight of the cylinder is greater than the buoyant force. This implies that the density of the cylinder is greater than the density of the liquid

Answer

The cylinder does not float because its density is greater than the density of the liquid, resulting in a weight that exceeds the buoyant force.

Key Concept

Archimedes' Principle: The buoyant force on an object is equal to the weight of the fluid displaced by the object.

Explanation

If the object's density is greater than the fluid's density, the object will sink because the buoyant force is not sufficient to counteract the object's weight.

Question 3: Calculate the density of the block of wood

Solution

a

Use the density formula:

\rho = \frac{m}{V}

b

Substitute the given values:

m = 180 \, \text{g}, \, V = 210 \, \text{cm}^3

c

Calculate the density:

\rho = \frac{180}{210} \approx 0.857 \, \text{g/cm}^3

Answer

0.857 g/cm³

Key Concept

Density:

\rho = \frac{m}{V}

Explanation

Density is the mass of an object divided by its volume. By substituting the given mass and volume, we can calculate the density.

Question 4: Predict and explain what happens when the block is released into the liquid

Solution

a

Compare the density of the block of wood (0.857 g/cm³) with the density of the liquid (0.88 g/cm³)

b

Since the density of the block is less than the density of the liquid, the block will float

c

The block will float because the buoyant force (equal to the weight of the displaced liquid) is greater than the weight of the block

Answer

The block will float because its density is less than the density of the liquid.

Key Concept

Archimedes' Principle: The buoyant force on an object is equal to the weight of the fluid displaced by the object.

Explanation

An object will float if its density is less than the density of the fluid it is placed in, as the buoyant force will be greater than the object's weight.

Question 5: Calculate the mass of the cylinder

Solution

a

Use the density formula:

\rho = \frac{m}{V}

b

Rearrange to solve for mass:

m = \rho V

c

Substitute the given values:

\rho = 9000 \, \text{kg/m}^3, \, V = 75 \, \text{cm}^3 = 75 \times 10^{-6} \, \text{m}^3

d

Calculate the mass:

m = 9000 \times 75 \times 10^{-6} = 0.675 \, \text{kg}

Answer

0.675 kg

Key Concept

Density:

\rho = \frac{m}{V}

Explanation

By rearranging the density formula, we can solve for mass using the given density and volume.

Question 6: Calculate the weight of the cylinder

Solution

a

Use the weight formula:

W = mg

b

Substitute the given values:

m = 0.675 \, \text{kg}, \, g = 10 \, \text{N/kg}

c

Calculate the weight:

W = 0.675 \times 10 = 6.75 \, \text{N}

Answer

6.75 N

Key Concept

Weight:

W = mg

Explanation

Weight is the product of mass and gravitational acceleration. By substituting the given mass and gravitational field strength, we can calculate the weight.

Question 7: State one way in which weight differs from mass

Solution

a

Weight is a force and depends on the gravitational field strength, while mass is a measure of the amount of matter in an object and is independent of gravity

Answer

Weight is a force that depends on gravity, while mass is a measure of matter and is independent of gravity.

Key Concept

Weight vs. Mass: Weight is the force exerted by gravity on an object, while mass is the amount of matter in the object.

Explanation

Weight varies with the gravitational field strength, but mass remains constant regardless of location.

Solution

a

Acceleration is a vector quantity. The two vector quantities in the list are force and impulse

b

(i) Use the equation of motion to calculate the speed at

t = 3.0

s:

v_f = v_i + at

Given:

v_i = 0 \, \text{m/s}

(initial velocity, since the car starts from rest)

a = 2.2 \, \text{m/s}^2

(acceleration)

t = 3.0 \, \text{s}

(time) Substitute the values:

v_f = 0 + (2.2 \, \text{m/s}^2 \times 3.0 \, \text{s}) = 6.6 \, \text{m/s}

c

(ii) Calculate the average speed of the car during the first 3.0 s: Average speed is given by:

\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}

Given: Total distance = 9.9 m Total time = 3.0 s Substitute the values:

\text{Average speed} = \frac{9.9 \, \text{m}}{3.0 \, \text{s}} = 3.3 \, \text{m/s}

d

(iii) Sketch a distance-time graph for the first 3.0 s of the journey: - The graph is a curve starting from the origin (0,0) and reaching the point (3.0 s, 9.9 m). - Since the car is accelerating uniformly, the graph will be a parabola opening upwards

Answer

a. Force and impulse

b(i). 6.6 m/s

b(ii). 3.3 m/s

b(iii). Parabolic curve from (0,0) to (3.0 s, 9.9 m)

Key Concept

Kinematics: Equations of motion for constant acceleration.

Explanation

The speed at a given time can be calculated using the equation

v_f = v_i + at

. The average speed is the total distance divided by the total time. The distance-time graph for uniformly accelerated motion is a parabola.

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