Question

In: Mechanical Engineering

A floating ball has a density (P») of 600 kg/m' and has a radius (R) of...

A floating ball has a density (P») of 600 kg/m' and has a radius (R) of 0.055 m. The equation that

gives the depth (x) to which the ball is submerged under water with a density (Pw) of 1000 kg/m

is given by:4

4/3*pi*R^3*pb*g=pi*x^2(R_x/3)*Pw*g

where the gravitational acceleration g = 9.81 m/s.

R

a) Use the false-position method to find the depth x to

which the ball is submerged under water within an

interval [0, 0.1]? Conduct three iterations only and find

the absolute relative approximate error at the end of

each iteration?

Water

Note: Summarize your results in one table and show one complete sample of calculations for one

iteration only.

b) If you would change the previous method to an open domain method to find the depth x; what

method would you select? Explain briefly (in English and without calculations), what would

you do and how would you do the computations.

Expert Solution

samet mamat answered 5 months ago

An average ping pong ball has a radius of r=0.019m and an average density of p=84kg/m3....

An average ping pong ball has a radius of r=0.019m and an average density of p=84kg/m3. The density of air is p=1.225kg/m3. a) what is the magnitude and direction in unit vector notation of the force required to hold it completely submerged in water? b) while still completely submerged , what is the difference in pressure between the top and bottom of the ball? C) if released, the ball will eventually find itself floating on the surface. What percent of...

A spherical bowling ball with mass m = 3.3 kg and radius R = 0.11 m...

A spherical bowling ball with mass m = 3.3 kg and radius R = 0.11 m is thrown down the lane with an initial speed of v = 8.9 m/s. The coefficient of kinetic friction between the sliding ball and the ground is ? = 0.28. Once the ball begins to roll without slipping it moves with a constant velocity down the lane. What is the magnitude of the angular acceleration of the bowling ball as it slides down the...

A uniform solid ball of m=4.0 kg and radius r rolls smoothly down a ramp. The...

A uniform solid ball of m=4.0 kg and radius r rolls smoothly down a ramp. The ball starts from rest. The ball descends a vertical height of 6.0 m to reach the bottom of the ramp. What is its speed at the bottom?

A bowling ball of mass m and radius r has a coefficient of static friction µ...

A bowling ball of mass m and radius r has a coefficient of static friction µ when in contact with an oiled wood surface. Model the ball as a solid uniform sphere. The surface is inclined at an angle θ with respect to the horizontal. What is the maximum angle of inclination of the surface such that the ball rolls without slipping? How does the angle change if the ball is now a hollow shell with all its mass concentrated...

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at...

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 17.2 s, to a final angular speed of ω = 31 rad/s. 1.What is the angular acceleration of the disk? 2. What is the angular displacement over the 17.2 s? 3. What is the moment of inertia of the disk? 4. What is the change in rotational energy of the disk?

A solid steel sphere of radius 1.50cm and density of 8045 kg/m³ was launched on a...

A solid steel sphere of radius 1.50cm and density of 8045 kg/m³ was launched on a horizontal frictionless surface. The sphere was launched using a spring gun which possessed a spring with a force constant of 35.6 N/m. The spring was compressed 30.0 cm and the sphere was launched. At the end of the frictionless surface (that was 0.955 m above the floor), the sphere rolled (no slipping) up a 25° ramp with height of 1.15m and then launched off...

What is the smallest number of whole logs (density = 735 kg/m³, radius = 0.077 m,...

What is the smallest number of whole logs (density = 735 kg/m³, radius = 0.077 m, length = 2.91 m) that can be used to build a raft that will carry 3 people, each of whom has a mass of 76.0 kg?

What is the smallest number of whole logs (density = 695 kg/m³, radius = 0.073 m,...

What is the smallest number of whole logs (density = 695 kg/m³, radius = 0.073 m, length = 2.73 m) that can be used to build a raft that will carry 6 people, each of whom has a mass of 87.5 kg?

A hollow ball has mass M=2.0kg, radius R=0.35m, and moment of inertia about the center of...

A hollow ball has mass M=2.0kg, radius R=0.35m, and moment of inertia about the center of mass I=(2/3)MR2. The ball is thrown without bouncing, to the right with an initial speed 2.0m/s and backspin. The hoop moves across the rough floor (coefficient of sliding friction = 0.25) and returns to its original position with a speed of 0.5 m/s. All surfaces and the hoop may be treated as ideally rigid. Develop an expression for angular velocity of the hoop as...

3. A block of wood has a mass of 3.67 kg and a density of 600...

3. A block of wood has a mass of 3.67 kg and a density of 600 kg/m3. It is to be loaded with lead so that it is still floating in water completely immersed. What mass of lead is needed (density of lead is 11,300 kg/m3)