A thin rod of length L = 3.00 m with variable mass density (x) = 3.00x² kg/m lies on the x-axis with one end at the origin. Where on the X-axis is the center of mass of this rod? {note this is a variable mass density} O 2.50 m O 1.50 m O 2.25 m O 2.70 m O 1.88 m SER
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- A 2.09-kg particle has a velocity (1.90 î – 2.90 j) m/s, and a 2.95-kg particle has a velocity (0.92 î + 6.01 j) m/s. (a) Find the velocity of the center of mass. |î + i) m/s (b) Find the total momentum of the system. i) kg · m/sA certain carbon monoxide molecule consists of a carbon atom of mass mc = 14 u and an oxygen atom of mass mo = 18 u that are separated by a distance of d = 122 pm, where "u" is an atomic unit of mass. a. Write a symbolic equation for the location of the center of mass of the carbon monoxide molecule relative to the position of the oxygen atom. This expression should be in terms of the masses of the atoms and the distance between them. b. Calculate the numeric value for the center of mass of carbon monoxide in units of pm.A rifle with a weight of 40 N fires a 4.5 g bullet with a speed of 290 m/s. (a) Find the recoil speed of the rifle. m/s(b) If a 725 N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle. m/s
- A knife thrower throws a knife toward a 300 g target that is sliding in her direction at a speed of 2.30 m/s on a horizontal frictionless surface. She throws a 22.5 g knife at the target with a speed of 38.0 m/s. The target is stopped by the impact and the knife passes through the target. Determine the speed of the knife (in m/s) after passing through the target.The pendulum apparatus in the video has a total mass of 578 grams. The pendulum rod has a small mass of 20 grams so you can treat all the mass of the pendulum as if it were hanging at the end which is called the “bob”. The mass of the rod should be taken into account in determining the center of mass of the apparatus which is 71.3 cm (not the length of the pendulum). A marble which hass a mass of 10 g is fired at the pendulum bob which has clay on it which allows the marble to stick to it. Derive a formula for measuring the velocity of the marble (vm) as a function of the mass of the marble mm, the mass of the marble/bob mmb and the velocity of the marble and bob vmb using the conservation of momentum.A 1.90-kg particle has a velocity (2.20 1 - 4.00 ĵ) m/s, and a 4.00-kg particle has a velocity (1.00 +8.00 ĵ) m/s. (a) Find the velocity of the center of mass. Î + m/s (b) Find the total momentum of the system. Î + J kg m/s
- A cue ball travelling at 0.785 m/s [270°] strikes a stationary five-ball, causing it to move at 0.601 m/s [230°]. The cue ball and the five-ball each have a mass of 160 g. What will be the velocity of the cue ball immediately after impact? Ignore frictional and rotational effects.An unfortunate astronaut loses his grip during a spacewalk and finds himself floating away from the space station, carrying only a rope and a bag of tools. First he tries to throw a rope to his fellow astronaut, but the rope is too short. In a last ditch effort, the astronaut throws his bag of tools in the direction of his motion, away from the space station. The astronaut has a mass of ma = 113 kg and the bag of tools has a mass of m the space station at v¡ = 1.80 m/s. = 10.0 kg. The astronaut is moving away from What is the minimum final speed Ubf of the bag of tools with respect to the space station that will keep the astronaut from drifting away forever? Ub,f = m/sYou're rolling solid rubber balls on the kitchen floor. Ball 1 has a density of 1.16 × 103 kg/m3 and a radius of 28.0 mm. Ball 2 has an unknown density and a radius of 43.0 mm and is initially at rest. You roll ball 1 at an initial speed of 3.00 m/s, and the two balls collide head-on. Ball 1 reverses direction and comes back to you at 2.00 m/s, and after the collision, the speed of ball 2 is 1.00 m/s. The positive x axis is in the direction of ball 1's initial motion. A.What is the magnitude of the initial momentum of ball 1? Express your answer with the appropriate units. B. What is the magnitude of the final momentum of ball 1? Express your answer with the appropriate units. C. What is the magnitude of the initial momentum of ball 2? Express your answer with the appropriate units.
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