The small washer is sliding down the cord OA. When it is at the midpoint, its speed is 28 m>s and its acceleration is 7 m>s2. Express the velocity and acceleration of the washer at this point in terms of its cylindrical components.

Velocity components

V_r = -16.28 m/s

V_z = -22.8 m/s

V_q = 0 m/s

Acceleration components

a_r = -4.07 m/s^2

a_z = -5.70 m/s^2

a_q = 0 m/s^2

Explanation:

Given:

- The diagram missing is attached.

- The speed of the washer v_o = 28 m/s

- The acceleration of washer a_o = 7 m/s^2

Find:

Express the velocity and acceleration of the washer at this point in terms of its cylindrical components.

Solution:

- From figure, compute the radial position r of washer in x-y plane:

                            r = sqrt ( 300^2 + 400^2 )

                            r = 500 mm

- From figure, compute the Length L of along the OA direction:

                            L = sqrt ( 500^2 + 700^2 )

                            r = 860 mm

- The radial and vertical components of velocity are:

                            V_r = V_o*cos(Q)

                            V_z = V_o*sin(Q)

Where, Q is the angle between OA and vector r.

                            V_r = 28*r/L = 28*500 / 860

                            V_r = -16.28 m/s

                            V_z = 28*700/L = 28*700 / 860

                            V_z = -22.8 m/s

                            V_q = 0 m/s

- The radial and vertical components of acceleration are:

                            a_r = a_o*cos(Q)

                            a_z = a_o*sin(Q)

Where, Q is the angle between OA and vector r.

                            a_r = 7*r/L = 7*500 / 860

                            a_r = -4.07 m/s^2

                            a_z = 7*700/L = 7*700 / 860

                            a_z = -5.70 m/s^2

                            a_q = 0 m/s^2

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.