-Four masses are placed along the x − a x i s as follows. A mass...

-Four masses are placed along the x − a x i s as follows. A mass of 2.0 k g is placed at x = 3.0 m, a mass of 6.0 k g is placed at x = 1.0 m, a mass of 4.0 k g is placed at x = − 2.0 m, and finally a mass of 1.0 k g is placed at x = − 4.0 m. Where is the center of mass of this system of masses?

-During a certain period of time, the angular position of a point object, rotating in a circular orbit of radius 2 m, is given by θ = 5 + 4 t + 2 t 2, where θ is in radians and t is in seconds. At t = 0, what are the magnitudes of the tangential component and the radial component of the acceleration of the point object?

-The mass of a car, including its four wheels, is 1000 kg. If all wheels have the same moments of inertia as four uniform disks of the same mass [10 kg each] and size as the wheels, what fraction of the total kinetic energy of the car is due to rotation of the wheels about their axles?

-A disc-shaped pulley, of mass 12 kg and radius 0.2 m, is wrapped around by a long string with one mass connected on each end. The part of the string that is connected to the larger mass has a tension of 5.0 N, while the part of the string connected to the smaller mass has a tension of 3.5 N. What is the angular acceleration, α, of the pulley?

Expert Solution

genius_generous answered 2 years ago

a) Four masses are placed on the x-axis so that the center of gravity is at...

a) Four masses are placed on the x-axis so that the center of gravity is at x = 0. A 1kg mass is placed at x = 1m, a 2kg mass is placed at x = 2m, a 3kg mass is placed at x = 3m, and lastly an unknown mass m4 is placed at x = −4m. What is the value of the unknown mass? b) If the unknown mass is doubled, what is the new x-coordinate of the...

Four identical masses of mass 700 kg each are placed at the corners of a square...

Four identical masses of mass 700 kg each are placed at the corners of a square whose side lengths are 15.0 cm. Part A) What is the magnitude of the net gravitational force on one of the masses, due to the other three? Part B) What is the direction of the net gravitational force on one of the masses, due to the other three? -toward the center of the square -outward the center of the square

The masses and coordinates of four particles are as follows: 45 g, x = 1.0 cm,...

The masses and coordinates of four particles are as follows: 45 g, x = 1.0 cm, y = 2.0 cm; 45 g, x = 0.0 cm, y = 4.0 cm; 25 g, x = -3.0 cm, y = -3.0 cm, 30 g, x = -1.0 cm, y = 4.0cm. What is the rotational inertia of this collection with aspect to the x-axis ( kg m2)? What is the rotational inertia of this collection with aspect to the y-axis? What is...

A body of mass 15.0 kg is traveling at 5.3 m/s along the positive x-axis with...

A body of mass 15.0 kg is traveling at 5.3 m/s along the positive x-axis with no external force acting. At a certain instant an internal explosion occurs, splitting the body into two chunks of 7.5 kg mass each. The explosion gives the chunks an additional 16 J of kinetic energy. Neither chunk leaves the line of original motion. Determine the speed and direction of motion of each of the chunks after the explosion. Enter the larger velocity. Enter the...

Four point masses each with a mass of 4.90 kg are positioned at the corners of...

Four point masses each with a mass of 4.90 kg are positioned at the corners of a rectangle with dimensions 1.80 meters by 3.00 meters. Assume these are the only masses that are gravitationally relevant. What is the magnitude of the gravitational force on a corner mass due to the other three masses?

A shaft carries four masses A, B, C and D placed in parallel planes perpendicular to...

A shaft carries four masses A, B, C and D placed in parallel planes perpendicular to the shaft axis and in this order along the shaft. The masses B and C are 40 Kg and 28 Kg and both are at 160 mm radius. While the masses in planes A and D are at 200 mm radius. Angle between B & C is 100°, B & A is 190° and both the angles being measured in the anticlockwise (mass B...

Four particles are in a 2-D plane with masses, x- and y- positions, and x- and...

Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y- velocities as given in the table below: m x y vx vy 1 7.6 kg -2.6 m -4.7 m 3 m/s -4.1 m/s 2 9.3 kg -3.5 m 3.6 m -4.9 m/s 5 m/s 3 8.9 kg 4.4 m -5.5 m -5.9 m/s 2 m/s 4 8.6 kg 5.4 m 2.5 m 4.2 m/s -2.9 m/s 1) What is the x position of...

Charges are placed on the x-axis as follows: q1 = + 5 μC at x =...

Charges are placed on the x-axis as follows: q1 = + 5 μC at x = -5 m q2 = − 3 μC at x = -1 m q3 = − 2 μ C at x = +2 m q4 = + 9 μ C at x = +3 m What is the net force on q2? Answer in units of milli-Newtons rounded to 3 significant figures.

Two solid objects, X and Y, of equal masses are placed in a molten lead bath...

Two solid objects, X and Y, of equal masses are placed in a molten lead bath and allowed to reach the bath temperature. (The objects themselves do not melt.) Each object is placed in a separate fish tank containing 1000 kg of water. Object X raises the water temperature by 20 °C while object Y raises the water temperature 80 °C. Which of the following is true? X has a larger specific heat than Y. Y has a larger specific...

A) Three identical very dense masses of 5000kg each are placed on the x axis. One...

A) Three identical very dense masses of 5000kg each are placed on the x axis. One mass is at x1 = -130cm , one is at the origin, and one is at x2 = 400 cm. 1) What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses? Take the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2N. Express your answer in newtons to three significant figures. 2) What...

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