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A bowling ball weighing 71.2 $\mathrm{N}$ is attached to the ceiling by a 3.80 $\mathrm{m}$ rope. The ball is pulled to one side and released; it then swings back and forth like a pendulum. As the rope swings through its lowest point, the speed of the bowling ball is measured at 4.20 $\mathrm{m} / \mathrm{s}$ . At that instant, find (a) the magnitude and direction of the acceleration of the bowling ball and (b) the tension in the rope. Be sure to start with a free-body diagram.

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Physics 101 Mechanics

Chapter 6

Circular Motion and Gravitatio

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

McMaster University

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Okay, so here we have a pendulum like situation on DH. They're here. We see that Ah, a boil is hanging from a rooftop and it's oscillating. And where when it's oscillating, that means it's making an ark and, ah, when it's exactly perpendicular to the horizontal, we are given the velocity at that point, so we know that if it's it's, um, it's oscillating. That means there's some force that's acting upwards. And also the radial acceleration of the born with is acting a force as well. So the radial acceleration is re squared over R and were given the radius and the velocity so we can figure out the radio exhibition from there. So re scared. Here is 4.2 meter per second. Then we were square, and then for our it's 3.8 meter, and from there we can find out the exploration as 4.64 meter per second, and it's in the upward direction right now for mass. We should know that mass should be weight of the ball divided by gravity, and ah, that's seven point 27 man now in the second part. So this is part in the second part, we'll start with the free body diagrams. So when the ball is at its minimum, um, we have we'll have to identify the forces that's acting on the ball. So let's say this is our ball. And if we considered right side as R exact sis and the perpendicular X is our Y axis, then the tension force that's acting on why access is team, and that will be counterbalanced by the gravitational force, gravitational pull and the force due to that. And also we have to remember that there's this relax elation that's acting upwards So and there's no there's no force on extraction, which and fakes this motion. So if we actually try toe sold for the Y direction forces, So that's our free body diagram. So that's actually move it aside. Um, so the forces that on the Y axis should be m times a Y. And from there we can right team. Now, this is pointing upwards, so T minus mg should be equal to the force due to this exhibition, which is mass times Canadian ex elation. And from there we consult for detention, which is end times G plus. Relax, elation, and we've already sold for the relax elation, and we know gravity so And we have already calculated mass in party. So this is 7.27 kilogram. Then we have 9.8 meters per second squared, plus 4.64 meters per seconds Group From there we get didn't smile, pours as 105 No, thank you.

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