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(II) It takes a force of 95.0 $\mathrm{N}$ to compress the spring of a toy popgun 0.175 $\mathrm{m}$ to "load" a $0.160-\mathrm{kg}$ ball. With what speed will the ball leave the gun if fired horizontally?

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$$10.2 \mathrm{m} / \mathrm{s}$$

02:26

Shital Rijal

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

Cornell University

Rutgers, The State University of New Jersey

Hope College

University of Winnipeg

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

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For this problem, on the topic of oscillators were told that a toy gun requires a force of 95 newtons in order to compress the spring 20.175 m. This is this allows the gun to load a 0.16 kg ball, and we want to know the speed at which the ball will leave the gun if it is then fired horizontally. Now the spring constant can be found from the ratio of the applied force to the displacement by hook's law, as K is equal to the supply force divided by the compression X. And the supply force is 95 Newton's divided by the compression of 0.175 meters. So the spring constant for the toy gun spring is 542 0.9 newtons per meter. Now, if we assume that there are no dissipated forces acting on the ball, the elastic potential energy in the loaded position will all become kinetic energy of the ball. So by the conservation of energy, the initial elastic potential energy must equally final kinetic energy so E I. Is equal to E. F. And so a half. Okay times the amplitude squared was equal to a half. M times the maximum velocity squared. So this means the maximum philosophy of the maximum speed at which the ball will leave the toy gun. V max is equal to the amplitude X max times the square root of K over em. And this is the amplitude zero point 175 m, the maximum compression and the square root of 542 0.9 newtons per meter, which is the spring constant calculated above, divided by the mass 0.16 kg. So calculating, we get the speed at which the ball will leave the toy gun to be 10 0.2 meters the second.

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