Using the following formulae (and only the following formulae), s = θr ; ω = v/r...
Using the following formulae (and only the following formulae), s = θr ; ω = v/r ; v = ds/dt ; ω = dθ/dt ; α = a/r ; a = dv/dt ; α = dω/dt ; α = ω^2 ; K = 1/2 mv^2 , derive the equation for the kinetic energy of an object moving in a circle with a constant tangential velocity in terms of m, ω, and r.
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Using the following formulae (and only the following formulae),
s = θr ; ω = v/r...
Lets begin with the assumption that R=kv. What are the units of the coefficient k in...
Lets begin with the assumption that R=kv. What are the units
of the coefficient k in terms of kilograms, metere, and/or
seconds?
dv 6. The equation of motion now becomes mº mg - Kv. dt This equation is also separable because all the terms involving v can be brought to the left side of the dv equation: 1 = 1. dig-(K/m) As before, we integrate both sides of the equation with respect to t and use a change of variables....
3) The velocity v(t) of a skydiver falling to the ground is governed by the equation...
3) The velocity v(t) of a skydiver falling to the ground is governed by the equation m dv/dt mg-kv, where g is the acceleration due to gravity, and k>0 is the drag constant associated with air resistance a) Find the analytical solution for V(t), assuming v(0) 0 b) Find the limit of v(t) as t goes to infinity. This is known as the terminal velocity. c) Give a graphical analysis of this problem, and re-derive the formula for the terminal...
In (14) of Section 1.3 we saw that a differential equation describing the velocity v of...
In (14) of Section 1.3 we saw that a differential equation describing the velocity v of a falling mass subject to air resistance proportional to the instantaneous velocity is dv dt where k> 0 is a constant of proportionality. The positive direction is downward (a) Solve the equation subject to the initial condition vo)o (b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass c) If the distance s measured from the point...
The kinetic energy, KE, for an object of mass m, moving at velocity v is represented...
The kinetic energy, KE, for an object of mass m, moving at velocity v is represented with the equation KE is equal to (1/2)(mass)(velocity)^2 Write the kinetic energy equation using a mathematical equation. Include: • The symbols for mass and velocity. • The Math Equation Function to write 1/2 in the fraction format. • Use the superscript format to write (velocity)^2.
Derive the expression for the initial velocity v of a ballistic pendulum in terms of the...
Derive the expression for the initial velocity v of a ballistic pendulum in terms of the swept-out angle theta. Use the following equations of momentum and energy conservation... When the projectile and the pendulum stick together, they have total mass m + M and we define their combined velocity to be V⃗ . The relationship from conservation of momentum is: mv = (m + M)V⃗ Conservation of energy requires the initial kinetic energy of the pendulum system to equal the...
The energy of motion is called: Kinetic energy. potential energy, inertial energy. Power. In an inelastic...
The energy of motion is called: Kinetic energy. potential energy, inertial energy. Power. In an inelastic collision: momentum is conserved. kinetic energy is conserved, both (a) and (b). If the velocity of a moving object is doubled and its mass is cut in half, the kinetic energy of the object is; remains the same, doubled quadrupled, cut in half. When the net work done on an object is speed of the object is me on an object is zero; the...
2. Consider the mass-spring system shown in the figure below. It can be shown that the...
2. Consider the mass-spring system shown in the figure below. It can be shown that the motion of the mass is governed by the equation a=-sw^2, where s and a are the position and acceleration of the mass, respectively, and w is a constant (which is referred to as the natural frequency of the system). Derive the equation describing the velocity of the mass in terms of the position. Assume that the velocity of the mass is v(subzero) when s=0...
Please help! :) Discussion #3 1. Consider the motion of an object that can be treated...
Please help! :)
Discussion #3 1. Consider the motion of an object that can be treated as a point particle and is traveling counter-clockwise in a circle of radius R. This motion can (and will for the purposes of these discussion activities) be described and analyzed using a Cartesian (x-y) coordinate system with a spatial origin at the center of the particle's circular trajectory (the physical path its motion traces out in space). (a) Draw a diagram of the position...
1.) In lecture, we developed the Maxwell-Boltzmann distribution given as: P(v)dv = 47 (2,16)"exp(-mv7/2kyn) v?dv Explicitly...
1.) In lecture, we developed the Maxwell-Boltzmann distribution given as: P(v)dv = 47 (2,16)"exp(-mv7/2kyn) v?dv Explicitly derive the following: a.) Show that this distribution is normalized. b.) For helium atoms at 500 K, use the error function in order to calculate the fraction of particles traveling in the range of 1500 m/s to 2000 m/s. c.) Produce an expression for <Vavy. (Note: Not the root square average as presented in lecture.) d.) Transform this distribution into a distribution in energy...
(30 pts) A D.C. motor is shown below, where the inductance L and the resistance R model the armat...
(30 pts) A D.C. motor is shown below, where the inductance L and the resistance R model the armature circuit. The voltage Vb represents the back-emf which is proportional to dθ/dt via K. The torque T generated by the motor is proportional to the i via a constant K. The inertia J represents the combined inertia of the motor and load. The viscous friction acting on the output shaft is B 1. pur voltaop a. A. (10 pts) Find the...
Lets begin with the assumption that R=kv. What are the units
of the coefficient k in terms of kilograms, metere, and/or
seconds?
dv 6. The equation of motion now becomes mº mg - Kv. dt This equation is also separable because all the terms involving v can be brought to the left side of the dv equation: 1 = 1. dig-(K/m) As before, we integrate both sides of the equation with respect to t and use a change of variables....
3) The velocity v(t) of a skydiver falling to the ground is governed by the equation m dv/dt mg-kv, where g is the acceleration due to gravity, and k>0 is the drag constant associated with air resistance a) Find the analytical solution for V(t), assuming v(0) 0 b) Find the limit of v(t) as t goes to infinity. This is known as the terminal velocity. c) Give a graphical analysis of this problem, and re-derive the formula for the terminal...
In (14) of Section 1.3 we saw that a differential equation describing the velocity v of a falling mass subject to air resistance proportional to the instantaneous velocity is dv dt where k> 0 is a constant of proportionality. The positive direction is downward (a) Solve the equation subject to the initial condition vo)o (b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass c) If the distance s measured from the point...
The kinetic energy, KE, for an object of mass m, moving at velocity v is represented with the equation KE is equal to (1/2)(mass)(velocity)^2 Write the kinetic energy equation using a mathematical equation. Include: • The symbols for mass and velocity. • The Math Equation Function to write 1/2 in the fraction format. • Use the superscript format to write (velocity)^2.
The energy of motion is called: Kinetic energy. potential energy, inertial energy. Power. In an inelastic collision: momentum is conserved. kinetic energy is conserved, both (a) and (b). If the velocity of a moving object is doubled and its mass is cut in half, the kinetic energy of the object is; remains the same, doubled quadrupled, cut in half. When the net work done on an object is speed of the object is me on an object is zero; the...
Please help! :)
Discussion #3 1. Consider the motion of an object that can be treated as a point particle and is traveling counter-clockwise in a circle of radius R. This motion can (and will for the purposes of these discussion activities) be described and analyzed using a Cartesian (x-y) coordinate system with a spatial origin at the center of the particle's circular trajectory (the physical path its motion traces out in space). (a) Draw a diagram of the position...
1.) In lecture, we developed the Maxwell-Boltzmann distribution given as: P(v)dv = 47 (2,16)"exp(-mv7/2kyn) v?dv Explicitly derive the following: a.) Show that this distribution is normalized. b.) For helium atoms at 500 K, use the error function in order to calculate the fraction of particles traveling in the range of 1500 m/s to 2000 m/s. c.) Produce an expression for <Vavy. (Note: Not the root square average as presented in lecture.) d.) Transform this distribution into a distribution in energy...
(30 pts) A D.C. motor is shown below, where the inductance L and the resistance R model the armature circuit. The voltage Vb represents the back-emf which is proportional to dθ/dt via K. The torque T generated by the motor is proportional to the i via a constant K. The inertia J represents the combined inertia of the motor and load. The viscous friction acting on the output shaft is B 1. pur voltaop a. A. (10 pts) Find the...
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