978-0073380308 Chapter 8 Solution Manual Part 22

Computation.

Substituting Eqs. (6) and (5) into Eqs. (1), (2), and (4), and taking into account Eq. (3), we

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Dynamics 2e 1869

Problem 8.124

A uniform bar

A

with a hook

H

at the end is dropped from rest as shown

from a height

dD3ft

over a fixed pin

B

. Letting the weight and length

of

A

be

WD100 lb

and

`D7ft

, respectively, determine the angle

✓

that

the bar will sweep through if the bar becomes hooked with

B

and does not

rebound. Although bar

A

becomes hooked with

B

, assume that there is no

friction between the hook and the pin.

Solution

First, we determine the impact speed between the bar and the pin

B

. Second, we determine the postimpact

angular velocity of the bar. Third, we determine of the angle swept by the bar.

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Force Laws.

Since the bar does not rebound away from the obstacle, we do not have a

COR

equation in

this problem.

Kinematic Equations.

Using the result from the work-energy part of the solution and using the parallel

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Dynamics 2e 1871

Problem 8.125

A drawbridge of length

`D30 ft

and weight

WD600 lb

is released in the position

shown and freely pivots clockwise until it strikes the right end of the moat. If the

COR

for the collision between the bridge and the ground is

eD0:45

and if the contact

point between the bridge and the ground is effectively

`

away from the bridge’s pivot

point, determine the angle to which the bridge rebounds after the collision. Neglect

any possible source of friction.

Solution

First, we determine the angular speed with which the bridge hits the ground. Second, we analyze the impact

between the bridge and the ground. Third, we determine the rebound angle.

To determine the angular speed of the bridge right before impact, we define

¿

and

¡

to be the positions at release and when the bridge first strikes the

ground respectively. We observe that, between

¿

and

¡

, the bridge is in a

We now proceed to determine the postimpact angular velocity of the bridge.

Balance Principles.

The impact-relevant

FBD

of the bridge illustrates the fact

that this is a constrained impact in which no momentum conservation principle can

be invoked.

Force Laws.

The only governing equation that can be written for this impact is the coefficient of restitution

equation long the

LOI

. Let

Q

be the point on the bridge that comes into contact with the ground. Then,

accounting for the fact that the ground does not move, we have

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Dynamics 2e 1873

Problem 8.126

A stick

A

with length

`D1:55

m and mass

mAD6kg

is in static equilibrium as

shown when a ball

B

with mass

mBD0:15 kg

traveling at a speed

v0D30 m=s

strikes the stick at distance

dD1:3

m from the lower end of the stick. If the COR for

the impact is

eD0:85

, determine the velocity of the mass center

G

of the stick, as

well as the stick’s angular velocity right after the impact.

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Computation.

Substituting Eq. (5), Eqs. (7), and the last of Eqs. (8) into Eqs. (1)–(4) and Eq. (6) we have

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Dynamics 2e 1875

Problem 8.127

A gymnast on the uneven parallel bars has a vertical speed

v0

and no angular speed when she grasps the

upper bar. Model the gymnast as a single uniform rigid bar

A

of weight

WD92 lb

and length

`D6ft

.

Neglecting all friction, letting

ˇD12ı

, and assuming that the upper bar

B

does not move after the

gymnast grasps it, determine the minimum speed

v0

for the gymnast to swing (counterclockwise) into the

horizontal position on the other side of the bar. Assume that, during the motion, the friction between the

gymnast’s hands and the upper bar is negligible.

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Balance Principles.

Applying the work-energy principle as a statement of conservation of energy, we have

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Dynamics 2e 1877

Problem 8.128

A uniform thin ring

A

of mass

mD7kg

and radius

rD0:5

m is released

from rest as shown and rolls without slip until it meets a step of height

`D0:45

m. Letting

ˇD12ı

and assuming that the ring does not

rebound off the step or slip relative to it, determine the distance

d

, such

that the ring barely makes it over the step.

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