Classical Mechanics Answers

1. A water tank is being towed by a truck on a level road, and the angle the free surface makes with the horizontal is measured to be 8 degrees. Determine the acceleration of the truck.

2. Consider two water tanks filled with water. The first tank is 8 m high and is stationary, while the second tank is 2 m high and is moving upward with an acceleration of 5 m/s². Which tank will have a higher pressure at the bottom?

3. A water tank is being towed on an uphill road that makes 14° with the horizontal with a constant acceleration of 3.5 m/s² in the direction of motion. Determine the angle the free surface of the water makes with the horizontal. What would your answer be if the direction of motion were downward on the same road with the same acceleration?

1. A 200-kg granite rock (p = 2700 kg/m³) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?

2. The hull of a boat has a volume of 180 m³, and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking (a) in a lake and (b) in seawater with a specific gravity of 1.03.

3. It is estimated that 90 percent of an iceberg’s volume is below the surface, while only 10 percent is visible above the surface. For seawater with a density of 1025 kg/m³, estimate the density of the iceberg.

4. The weight of a body is usually measured by disregarding buoyancy force applied by the air. Consider a 20-cm-diameter spherical body of density 7800 kg/m³. What is the percentage error associated with the neglecting of air buoyancy?

1. The cart is allowed to roll freely down the inclined plane due to its weight. Show that the slope of the surface of the liquid, theta. during the motion is theta = phi.

2. The cart is given a constant acceleration a up the inclined plane. Show that the lines of constant pressure within the liquid have a slope of tan theta = (a cos phi)/ (a sin phi + g).

3. A large container of benzene is transported on the truck. Determine the level in each of the vent tubes A and B if the truck accelerates at a = 1.5 m/s². When the truck is at rest, h_A = h_B = 0.4 m.

4. A woman stands on a horizontal platform that is rotating at a constant angular velocity w. If she is holding a cup of tea, and the center of the cup is 0.9 m from the axis of rotation, determine w if the slope angle of the liquid's surface is 5°. Neglect the size of the cup.

1. The hot-air balloon contains air having a temperature of 80 degrees Celsius, while the surrounding air has a temperature of 20 degrees Celsius. Determine the volume of hot air if the total mass of the balloon and the load is 770 kg. 

2.Water in the container is originally at a height of h = 1m. If a block having a density of 800 kg/m³ is placed in the water, determine the new level h of the water. The base of the block is 600 mm square, and the base of the container is 1.2 m square.

Discuss the motion of a simple pendulum under the fol lowing initial conditions. (i) At t=0, its displacement=0 and its velocity is vo (ii) At 1-0, its displacement is x and its velocity is vo

The frequency range of audible sound is [Best

answerl.

A. lower than 20 Hz.

B. lower than 20 KHz.

C. between 20 Hz to 20 KHz.

D. greater than 20 MHz.

[Best answer] is NOT electromagnetic wave.
A. Light
B. Microwaves
C. X-rays
D. Sound wave

An apple is falling down from a height of 20m and then hit a

person. Assume that the mass of the apple is 200g. The

duration of impact is 0.001 sec and that the area of the

bone is 1 cm². (a) Calculate the impulsive force applied to

the person. (b) If the rupture strength for body tissue is

about 5 X 10⁶ dyn/cm² will the impact force lead to serious

injury for the person?

In a car collision, the bag expands suddenly and cushions

the impact of the passenger. Assume the impact velocity is

105 km/h. For a 70-kg person with a 30-cm allowed

stopping distance, (a) calculate the stopping force per cm²

applied to the person, if the average applied force is

uniformly distributed over a 1000-cm² area of the

passenger's body. (b) calculate the duration of the collision

between the passenger and the inflated bag of the collision

protection device. (c) If the rupture strength for body tissue

is about 5 X 10⁶dyn/cm², will the impact force lead to

serious injury for the passenger?

Sound waves in air are [Best answer].

A. Transverse waves

B. Longitudinal waves

C. Shear waves

D. Stress waves