# Question 6.6: An amusement park ride shown in Fig. 6.3 consists of a 20 ft...

An amusement park ride shown in Fig. 6.3 consists of a 20 ft diameter cylindrical room that turns about its axis. People stand again st the rough cylindrical wall. After the room has reached a certain angular speed, the floor drops from under the riders. What must be the angular speed of the room to assure that a person will not slide on the wall? The design coefficient of static friction is μ = 0.4 .

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Question: 6.14

## A pendulum bob B attached to a rigid rod of negligible mass and length ℓ is  suspended from a smooth movable support at O that oscillates about the natural undeformed state of the spring so that x(t) = Xo sin Ωt in Fig. 6.19. Apply equation (6.80) to derive the equation of motion for the bob. ...

The forces that act on the pendulum bob B are show...
Question: 6.16

## Determine the Coriolis deflection of a projectile fired eastward at latitude λ. Derive the classical relations for the motion and the range when the Earth’s rotation is neglected. ...

Since the projectile is fired due east (the j dire...
Question: 6.15

## The equation for the undamped, forced vibration of the pendulum device described in Fig. 6.19, page 150, is given in (6.81e). Solve this equation for the case when both the motion of the hinge support and the angular motion of the pendulum are small. Assume that the pendulum is released from rest ...

The differential equation (6.8Ie) describes a comp...
Question: 6.11

## Falling body with air resistance. A particle of mass m, a raindrop for example, falls from rest through the atmosphere. Neglect the Earth’s motion, wind effects, and the buoyant force of air, and adopt Stokes’s law to model the air resistance. Determine as functions of time the rectilinear speed ...

The solution may be read from the foregoing result...
Question: 6.12

## Projectile motion with air resistance. A projectile S of mass m is fired from a gun with muzzle speed Vo at an angle β with the horizontal plane. Neglect the Earth’s motion and wind effects and assume that air resistance is govern ed by Stokes’s law. Determine the projectile’s motion as a function ...

The equations of motion with air resistance govern...
Question: 6.10

## Arnold Aardvark is sunbathing on a lookout platform at xo = ai + bj in the frame Φ = {O; ik } when he spots Percy Panther at 0 preparing to fire an artillery gun pointed directly toward the platform, as shown in Fig. 6.5. The gun has a muzzle velocity vo and the tower is well within its range r . ...

The free body diagrams of the shell S and Arnold A...
Question: 6.9

## Percy Panther is snoozing in an open-top artillery truck when he senses the presence of the mischievous Arnold Aardvark lurking beneath. He quietly releases the handbrake to escape down the hill inclined at an angle α. Arnold Aardvark having quietly rigged a remote trigger, immediately fires the ...

First, we determine the motion of the shell S, who...
Question: 6.8

## A relativistic particle P, initially at rest at the origin in frame ψ, is moving along a straight line under a constant force Fo. Determine the relativistic speed and the distance traveled by P as functions of time. ...

The equation of motion for the relativistic partic...
Question: 6.7

## A particle P in an inertial reference frame has an initial velocity vo at the place xo, and subsequently moves under the influence of a force that is proportional to the time and acts in a fixed direction e. Find the position and velocity of P at time t . ...

The force on P is given by  \mathbf{F}(P, t...