A vehicle on a monorail has a speed S = 10 m/s and an acceleration S=4m/s 2 relative to the ground reference XYZ when it reaches point A. Inside the vehicle, a 3 kg mass slides along a rod which at the time of interest is parallel to the X axis. This rod rotates about a vertical axis withw=1 rad /s and w=2 rad/s 2 relative to the vehicle at the time of interest. Also at this time, the radial distance d of the mass is .2 m and its radial velocity v =.4 m/s inward. What is the dynamic force on the mass at this instant?

Question

A vehicle on a monorail has a speed S = 10 m/s and an acceleration S=4m/s 2 relative to the ground reference XYZ when it reaches point A. Inside the vehicle, a 3 kg mass slides along a rod which at the time of interest is parallel to the X axis. This rod rotates about a vertical axis withw=1 rad /s and w=2 rad/s 2 relative to the vehicle at the time of interest. Also at this time, the radial distance d of the mass is .2 m and its radial velocity v =.4 m/s inward. What is the dynamic force on the mass at this instant?

Answer 1

Pls anr give me

Answer 2

How can there be two values of w at the same time? Is one of those two numbers (1 and 2) an angular acceleration?

Answer 3

To find the dynamic force on the mass at this instant, we need to consider the inertia force and the centripetal force acting on the mass.

First, let's calculate the inertia force. The inertia force is the force experienced by an object due to its acceleration relative to an accelerating reference frame.

Given:
Mass of the object (m) = 3 kg
Acceleration relative to the ground reference (a) = 4 m/s^2

The inertia force (F_inertia) can be calculated using the formula:
F_inertia = m * a

Substituting the given values:
F_inertia = 3 kg * 4 m/s^2
F_inertia = 12 N

Next, let's calculate the centripetal force. The centripetal force is the force that keeps an object moving in a circular path. It is given by the formula:

F_centripetal = m * (ω^2) * r

Given:
Radial distance (r) = 0.2 m
Radial velocity (v) = 0.4 m/s inward
Angular velocity relative to the vehicle (ω) = 1 rad/s
Angular acceleration relative to the vehicle (α) = 2 rad/s^2

To calculate the angular acceleration (α), we can use the formula:
α = (dv/dt) / r

Given:
dv/dt = -0.4 m/s / 1 s = -0.4 rad/s

Substituting the given values:
α = -0.4 rad/s / 0.2 m
α = -2 rad/s^2

Now, we can calculate the centripetal force:
F_centripetal = 3 kg * (1^2) * 0.2 m
F_centripetal = 0.6 N

Finally, we can find the total dynamic force on the mass by adding the inertia force and the centripetal force:
Total dynamic force = F_inertia + F_centripetal
Total dynamic force = 12 N + 0.6 N
Total dynamic force = 12.6 N

Therefore, the dynamic force on the mass at this instant is 12.6 N.