A small ball swings in a horizontal circle at the end of a cord of length
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Vector Mechanics for Engineers: Dynamics
- Three 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_forward1. 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_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
- I 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_forwardBall B (v) with a mass of 2.0 kg is rotating in an orbit of r = 0.8 m with a velocity = = 2.4 m / s. From this moment on, find the velocity of ball B at the moment when r is 0.5 m since the rope attached to it is pulled as shown in the figure with v, = 1.2m / s. Also calculate the work required to pull the rope.arrow_forwardFind the magnitude and direction of the velocity at point B.arrow_forward
- there is a spring with k=0.9 N/m conected to arm AB which is 15 kg when angle 0 spring is uncompressed. if we release arm AB from rest when angle=0 what will its angular velocity when angle is 30 its moving on vertical planearrow_forwardQ2/ The slotted arm revolves about a normal axis through point O with a constant angular velocity w.The path radius of the center of the pin A varies according to r = 20+ 2sin(nwt)where n is the number of lobes = 6 in this case. pin A If w=12 rad/s, and the spring compression varies from 11.5 N to 19.1 N, calculate the force R between the cam and the 0.1 kg pin A when it passes over the top of the lobe in the position shownarrow_forward3/218 A 0.4-kg particle is located at the position r, = 2i + 3j + k m and has the velocity v =i+j+ 2k m/s at time t = 0. If the particle is acted upon by a sin- gle force which has the moment Mo = (4 + 21)i + (3 -j + 5k N-m about the origin O of the Coordinate system in use, determine the angular momentum about O of the particle when t = 4 s.arrow_forward
- People A and B are fixed on a frictionless disk with radius R= 4 (m) and rotating at an angular velocity o= 3 (rad/s) as shown in the figure. As shown in the figure, person A in the center throws the ball in his hand at v = 8 (m/s) so that the person B can catch the ball. Since the image given in the figure shows t=0 (s), after how many seconds should person A throw the ball so that pers on B can catch it? Take T=3. 1= 0 В A. v R A) 0.35 В) 0.55 С) 0.75 D) 1.2 E) 0.50arrow_forwardWith a mass of 2.0 kg, the ball B (vB1) = 2.4m/s and rotates in an orbit with a radius of r1 = 0.8 m. From this moment on, the rope attached to it is 1.2m / s. Find the velocity of ball B at the moment r2 D 0.5 m since it is pulled with its velocity Vr = as shown in the figure. Also calculate the work required to pull the rope. %3Darrow_forwardI need a simple solutionarrow_forward
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