Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,...
Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt=-kv .It is known that a body’s initial velocity Vo is observed at location Xo.
a.Estimate the body’s velocity and the position at any time t > 0.
b.Conclude that the body travels only a finite distance and determine that distance.
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Suppose that a body moves through a resisting medium with
resistance proportional to its velocity v,...
feet per second and in miles per second 18 An object of mass m is moving...
feet per second and in miles per second 18 An object of mass m is moving horizontally through a medium which resists the motion with a force that is a func- tion of the velocity; that is, d's dv f(v) dt =m dt2 where v = s(1) represent the velocity and at time , respectively. For example, v(t) and s position of the object think of a boat moving through the water. (a) Suppose that the resisting force is proportional...
2 A particle falling from rest in a vertical line in a medium with resistance kv...
2 A particle falling from rest in a vertical line in a medium with resistance kv per unit mass, k is a constant, v is the velocity at any time and position x, prove that it acquires a speed 9. -2kh 1 - e T is the terminal velocity given by a distance h, where in falling through T A particle projected upwards in the same medium with initial speed V, and returns to the point of projection with speed...
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...
A mass of 1.25kg stretches a spring 0.05m. The mass is in a medium that exerts a viscous resistance of 192N when the mass has a velocity of 6m/s. The viscous resistance is proportional to the speed of...
A mass of 1.25kg stretches a spring 0.05m. The mass is in a medium that exerts a viscous resistance of 192N when the mass has a velocity of 6m/s. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.06m and released. Find a function u(t) to express the object's displacement from the spring's natural position, in m after t seconds. Let positive displacements indicate a stretched spring, and use 9.8m/s^2 as...
Submission 3 (0.66/1 points) Friday, July 24, 2020 07:15 PM +08 Suppose a small cannonball weighing...
Submission 3 (0.66/1 points) Friday, July 24, 2020 07:15 PM +08 Suppose a small cannonball weighing 98 N is shot vertically upward, with an initial velocity Vo = 94 m/s. The answer to the question "How high does the cannonball go?" depends on whether we take air resistance into account. If air resistance is ignored and the positive direction is upward, then a model for the state of the cannonball is given by d s/dt = -9 (equation (12) of...
If a body of mass m falling from rest under the action of gravity encounters an...
If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into dv the fall satisfies the differential equation m- mg-kv, where k is a constant that depends on the body's aerodynamic properties and the density of the air. (Assume dt that the fall is short enough so that the variation in the air's density will not affect the outcome...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same in...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for...
(3) A body moving so that,at time t,it's mass is m, it's velocity is v and...
(3) A body moving so that,at time t,it's mass is m, it's velocity is v and the resultant force acting on the body is F. Suppose that at this instant, a particle of mass om and velocity u coaleces with the body so that, at time ot, the body has the mass m + Sm and the velocity v + öv. Prove that Fma (v- D-u a. A body with initial mass rn is projected vertically upwards with speed where...
20. Suppose an object moves so that its velocity at time t is described by the...
20. Suppose an object moves so that its velocity at time t is described by the function v(t) = t2 – 8t + 7. Express the total distance traveled by the particle from time t=0 to 1= 4 using an integral or combination of integrals. Then evaluate the integral(s) to determine the solution. You are allowed to use the integration capabilities of a graphing calculator to evaluate the integral(s).
1 In many fluids, the flow velocity is observed to vary linearly from zero at the...
1 In many fluids, the flow velocity is observed to vary linearly from zero at the bottom to u at the top. Moreover, the magnitude F of the force acting on the top plate is found to be proportional to the speed and the area A of eaclh plate, and inversely proportional to their distance separation y The proportionality factor μ is the viscosity of the fluid. Using the above equation find out the dimensions of (10 pts.) A car...
feet per second and in miles per second 18 An object of mass m is moving horizontally through a medium which resists the motion with a force that is a func- tion of the velocity; that is, d's dv f(v) dt =m dt2 where v = s(1) represent the velocity and at time , respectively. For example, v(t) and s position of the object think of a boat moving through the water. (a) Suppose that the resisting force is proportional...
2 A particle falling from rest in a vertical line in a medium with resistance kv per unit mass, k is a constant, v is the velocity at any time and position x, prove that it acquires a speed 9. -2kh 1 - e T is the terminal velocity given by a distance h, where in falling through T A particle projected upwards in the same medium with initial speed V, and returns to the point of projection with speed...
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...
Submission 3 (0.66/1 points) Friday, July 24, 2020 07:15 PM +08 Suppose a small cannonball weighing 98 N is shot vertically upward, with an initial velocity Vo = 94 m/s. The answer to the question "How high does the cannonball go?" depends on whether we take air resistance into account. If air resistance is ignored and the positive direction is upward, then a model for the state of the cannonball is given by d s/dt = -9 (equation (12) of...
If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into dv the fall satisfies the differential equation m- mg-kv, where k is a constant that depends on the body's aerodynamic properties and the density of the air. (Assume dt that the fall is short enough so that the variation in the air's density will not affect the outcome...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for...
(3) A body moving so that,at time t,it's mass is m, it's velocity is v and the resultant force acting on the body is F. Suppose that at this instant, a particle of mass om and velocity u coaleces with the body so that, at time ot, the body has the mass m + Sm and the velocity v + öv. Prove that Fma (v- D-u a. A body with initial mass rn is projected vertically upwards with speed where...
20. Suppose an object moves so that its velocity at time t is described by the function v(t) = t2 – 8t + 7. Express the total distance traveled by the particle from time t=0 to 1= 4 using an integral or combination of integrals. Then evaluate the integral(s) to determine the solution. You are allowed to use the integration capabilities of a graphing calculator to evaluate the integral(s).
1 In many fluids, the flow velocity is observed to vary linearly from zero at the bottom to u at the top. Moreover, the magnitude F of the force acting on the top plate is found to be proportional to the speed and the area A of eaclh plate, and inversely proportional to their distance separation y The proportionality factor μ is the viscosity of the fluid. Using the above equation find out the dimensions of (10 pts.) A car...
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