An automobile tire is shown in the figure below. The tire is made of rubber with a uniform density of 1.10 ✕ 103 kg/m3. The tire can be modeled as consisting of two flat sidewalls and a tread region. Each of the sidewalls has an inner radius of 16.5 cm and an outer radius of 30.5 cm as shown, and a uniform thickness of 0.645 cm. The tread region can be approximated as having a uniform thickness of 2.50 cm (that is, its inner radius is 30.5 cm and outer radius is 33.0 cm as shown) and a width of 21.2 cm. What is the moment of inertia (in kg · m2) of the tire about an axis perpendicular to the page through its center?

One of the concrete pillars that supports a house is 2.6 m tall and has a radius of 0.54 m. The density of concrete is about 2.2 x 10^3 kg/m^3. Find the weight of this pillar in pounds (1 N = 0.2248 lb). Express your answer in whole numbers.

It is known that a cubical object made of cast aluminum 0.213 m on a side contains a hollow cavity also in the shape of a cube but of unknown dimensions. If the mass of the object is 22.8 kg, determine the length of each side of the interior cubical cavity. The density of aluminum is 2.70  103 kg/m3.

One end of a wire is attached to a ceiling, and a solid brass ball is tied to the lower end. The tension in the wire is 449 N. What is the radius of the brass ball?

Need Help: It is known that a cubical object made of cast aluminum 0.213 m on a side contains a hollow cavity also in the shape of a cube but of unknown dimensions. If the mass of the object is 22.8 kg, determine the length of each side of the interior cubical cavity. The density of aluminum is 2.70  103 kg/m3. Given Tip: How is the volume of the cubical object related to the volume of aluminum in the object and the volume of the cubical cavity? How is the mass of the cubical object related to the mass of aluminum in the object? Recall how the volume of a cube is related to the length of each side of the cube.

The human mandible (lower jaw) is attached to the temporomandibular joint (TMJ). The masseter muscle is responsible for pulling the mandible upward when you are talking or eating. It is attached at a horizontal distance of about 2.70 cm from the TMJ. The horizontal distance from the TMJ to your incisors is 6.60 cm. If the masseter muscle exerts a force of 182 N on your mandible when you bite into an apple at a constant rate, then what is the magnitude of the force exerted by your incisors on your food, assuming that both forces are vertical?

There are three cylindrical vases on the table, none of them is taller than 40 cm. The firstvase can be filled with 2 dl of water, the second one with 3 dl, and the third with more than 6 dl water. The area of the cross section of the first vase is 10 cm^2, the area of the cross section of the other two vases is 20 cm^2. There is the same amount (volume) of water in each vase. It can be observed that if a specific tuning fork is placed just above the vases, its sound is getting louder. The width of the bottom of each vase is 1 cm, the speed of sound in air is 340 m/s, and the frequency of the tuning fork is less than 1 kHz. a) What is the volume of water in the vases? b) What is the frequency of the tuning fork? c) What is the height of the third vase?

A uniform rod has mass m and length L. One end of the rod is attached to a fixed point O by a hinge and an additional force F is applied to the other end of the rod in the horizontal direction shown. 30° mg magnitude of applied force = Given that the rod is in mechanical equilibrium, what is the magnitude of the applied force F, expressed as a numerical multiple of mg, where g is the magnitude of the acceleration due to gravity? Express your answer by entering a decimal number, specified to 3 significant figures, into the empty box below. F x mg.

A straight rod has one end at the origin and the other end at the point (L,0) and a linear density given by λ=ax^2, where a is a known constant and x is the x coordinate. Since this wire is not uniform, you will have to use integration to solve this part. Use M=∫L0dm to find the total mass M. Find xcm for this rod. Express your answer in terms of one or both of a and L.

Calculate the mass of a solid gold rectangular bar that has dimensions Iwh = 4.80 cm x 12.0 cm x 25.0 cm. (The density of gold is 19.3 x 103 kg/m³.) kg