978-0073380308 Chapter 3 Solution Manual Part 4

436 Solutions Manual

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Dynamics 2e 437

Problem 3.23

A metal ball with mass

mD0:15 kg

is dropped from rest in a ﬂuid. The magnitude

of the resistance due to the ﬂuid is given by

Cdv

, where

Cd

is a drag coefficient

and

v

is the ball’s speed. If

CdD2:1 kg=s

, determine the ball’s speed

4

s after

release.

Solution

To determine the ball’s speed we need to determine the ball’s acceleration. In turn, we can

determine the ball’s acceleration by applying Newton’s second law. We model the ball as a particle

438 Solutions Manual

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Dynamics 2e 439

Problem 3.24

A metal ball weighing

0:35 lb

is dropped from rest in a ﬂuid. The magnitude of the

resistance due to the ﬂuid is given by

Cdv

, where

Cd

is a drag coefficient and

v

is

the ball’s speed. It is observed that

2

s after release, the speed of the ball is

25 ft=s

.

Determine the value of Cd.

Solution

440 Solutions Manual

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

Dynamics 2e 441

Problem 3.25

A horse is lifting a

500 lb

crate by moving to the right at a

constant speed

v0D3ft=s

. Observing that

B

is fixed and

letting

hD6ft

and

`D14 ft

, determine the tension in the

rope when the horizontal distance

d

between

B

and point

A

on the horse is

10 ft

. Treat all rope segments between

B

and

C

as vertical, and ignore the change in the amount of rope that

wraps around the pulley at B.

Solution

We neglect the inertia of the pulleys and the cord as well as the horizontal motion of

the crate. We model the cord as inextensible and the crate as a particle. Performing an

442 Solutions Manual

Problem 3.26

The centers of two spheres

A

and

B

with masses

mAD1kg

and

mBD2kg

are a distance

r0D1

m apart.

B

is fixed in space, and

A

is initially at

rest. Using Eq. (1.5) on p. 3, which is Newton’s universal law of gravitation,

determine the speed with which

A

impacts

B

if the radii of the two spheres are

rAD0:05

m and

rBD0:15

m. Assume that the two masses are infinitely far

from any other mass so that they are only inﬂuenced by their mutual attraction.

Solution

Dynamics 2e 443

Problem 3.27

Spring scales work by measuring the displacement of a spring that supports

both the platform and the object, of mass

m

, whose weight is being measured.

Neglect the mass of the platform on which the mass sits and assume that the

spring is uncompressed before the mass is placed on the platform. In addition,

assume that the spring is linear elastic with spring constant k.

If the mass

m

is gently placed on the spring scale (i.e., it is released from

zero height above the scale), determine the maximum reading on the scale after

the mass is released.

Solution

The scale’s reading is the value of the spring force supporting the platform. The latter is

determined by the position of the weight placed on the platform. This implies that we need

444 Solutions Manual

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Dynamics 2e 445

Problem 3.28

Spring scales work by measuring the displacement of a spring that supports

both the platform and the object, of mass

m

, whose weight is being measured.

Neglect the mass of the platform on which the mass sits and assume that the

spring is uncompressed before the mass is placed on the platform. In addition,

assume that the spring is linear elastic with spring constant k.

If the mass

m

is gently placed on the spring scale (i.e., it is released from

zero height above the scale), determine the maximum speed attained by the

mass mas the spring compresses.

Solution

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