A small ball swings in a horizontal circle at the end of a cord of length
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Vector Mechanics For Engineers
- Three identical point masses of m =0.2 (kg) are moving at a constant velocity v =20 (m/s) equidistant from each other on a circular orbit of radius R = 0.3 (m). What is the total angular momentum (kg.m²/s) of the three point masses relative to point A at the moment shown in the figure. Point A is 2R away from the center. m 2R m a: m A) 0.9 В) 1.2 С) 1.8 D) 3.0 E) 3.6arrow_forwardA 10-kg mass rotates around the vertical pole in a horizontal, circular path of radius R = 1 m. If the magnitude of the velocity is v= 3 m/s, what are the tensions in the strings A and B? 35 B 350 Aarrow_forwardThree identical point masses of m = 0.1 (kg) are moving at a constant velocity v=10 (m/s) equidistant from each other on a circular orbit of radius R = 0.4 (m). What is the total angular momentum (kg.m²/s) of the three point masses relative to point A at the moment shown in the figure. Point A is 2R away from the center. m 2R A m R m A) 0.9 В) 1.2 С) 1.8 D) 3.0 E) 3.6arrow_forward
- 1. A wood block of mass mw = 200 g is projected from the ground at a speed vo = 35 m/s and at an angle 60 = 50°. When at height h= 24 m the wood block was hit by a bullet of mass m = 25 g which was moving at v= 220 m/s and at an angle 6 = 70°. After the collision, the bullet embedded itself in the block and move together and land at point A on the ground. Then they move on the ground that has coefficient of kinetic friction u: = 0.5 and start to compress a horizontal spring at point B. The distance between point À and B is 18 m and the spring constant k = 3x10? N/m. Right end of the spring is fixed, and all motions are confined in x-y plane. Wood block + Bullet Bullet Wood B block (a) Was the collision between the wood block and the bullet elastic or inelastic? Explain quantitively. (b) Find the maximum height from the ground the block with the bullet reached. (c) How far is point A from the launch point of the wood block? (d) Calculate the velocity at which the block-bullet system…arrow_forwardAs in the figure, in an amusement vehicle rotating in the amusement park, the center shaft rotates at a speed of n=7 rpm. Meanwhile, the child is moved with the position equations r = (2 sinθ + 5) m and z = (3 cosθ) m. Find the forces generated in the child in all three axes (r, θ, z). The weight of the child is m = 34 kg. At the time the photo was taken, θ=123 degrees.arrow_forward1. Produce free body diagrams and equations of motion for each moving coordinate in the following diagrams. X k₁ DE PAR k₁ k₂ k₂ ww (b) (a) X Farrow_forward
- A particle M1, weighing 2.4 Ibs, is tied to a thread and describes a circular path in a horizontal plane. The thread, of negligible mass, passes through a hole in the center of the circle and descends vertically. Another particle M2 is attached, weighing 5.0 Ibs, as shown in the figure. If M1 describes a uniform circular motion, with angular velocity w 3.1 rad/s, determine the radius R of the circumference in inches.arrow_forwardI Suppose an autonomous surface vessel (ASV) traveling with velocity TvG/O= vi₁ begins to make a turn by adjusting the thrust of its left and right thrusters, TA and TB, respectively. The center of mass of the ASV is located at G and the ASV is symmetric about its vertical axis. The ASV also experiences a drag force that is proportional to its speed and opposes its velocity. At the instant shown, the drag force is D = -kvi₁ where k is a drag coefficient. 1. To model the mass moment of inertia, approximate the ASV as consisting of three rigid bodies: a flat plate as a center body of mass 6m and two slender rods housing the propulsion assemblies, each of mass m, at the outboard sides of the vehicle. Determine the mass moment of inertia, IG, about the vertical axis passing through the center of mass G. (Hint: Use the parallel axis theorem.) 2. At the instant shown, determine the inertial acceleration vector ac/o = axi₁ + ayi2 of the center of mass and the angular acceleration a of the…arrow_forwardThree identical point masses of m = 0.3 (kg) are moving at a constant velocity v =10 (m/s) equidistant from each other on a circular orbit of radius R= 0.2 (m). What is the total angular momentum (kg.m/s) of the three point masses relative to point A at the moment shown in the figure. Point A is 2R away from the center. m 2R m marrow_forward
- Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z-position of 2.3 x 106 m through the center of a planet with radius 7.6 x 106 m. If the mass of the planet is 33.9 x 1015 kg, measure the displacement of the ball at time t = 9 s?arrow_forwardTwo flywheels are pinned to opposite ends of a metal bar. The smaller flywheel has a mass of 40 kg and a radius of 0.25 m. The larger flywheel has a mass of 275 kg and a radius of 1.75 m. The bar has a mass of 2 kg and a length of 3 m. A wooden plate acts as a ripcord by temporarily pressing it against the flywheels and rapidly translating it to the left at v = angular velocity of 25 rad/s and the large flywheel has an angular velocity of 3.5714285714286 rad/s. The flywheel-bar assembly is then set on frictionless ice such that the axes of rotation are perpendicular to the ice surface. 6.25 m/s. The plate is removed when the small flywheel has an The flywheel pins have Hk = 0.05, which eventually causes the flywheels to stop spinning relative to the metal bar. Angular momentum is conserved, so the whole assembly continues spinning as a rigid body about the center of mass. What is the final angular velocity of the assembly? rad/s. The flywheels and bar rotate about their combined center…arrow_forward4. A loading car is at rest on a track forming an angle of 25° with the vertical when a force is applied to the cable attached at C. The gross weight of the car and its load is 5465 lb WG, and it acts at point G. Know the tension in the cable connected at C is 5000 Ib Tc. Neglect friction between the car and the track. Determine how far the car travels in 15 seconds. Model this as a particle at G. 24 in. B 25 in. 30 in. 25 in.arrow_forward
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