# Physics - practice problem set - 5 problems

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Homework 5-1

Due date: Mon 22 Mar 2004 09:00:00 AM MST

18 point(s)

Pulling Out Tree Stump

You are in a truck trying to pull out a tree stump. The mass

of the tree stump m is 170.0 kg. You have attached the winch

at the front of the truck to the tree as shown in the diagram

below:

As you try to pull out the stump with the truck, the winch ex-

erts a time dependant force with magnitude: Fws(t) = F0ebt

where F0 and b are constants, and t is the time since the

winch began pulling. If the force necessary to remove the

trunk is Fout, how long will it take to pull out the stump?

Use the following values in your calculation: F0 = 20.0 N

b = 4.1 s��1

Fout = 17000.0 N

= 51.0 degrees

tout =

You are correct. Your receipt is 480-1079

Find the work done on the stump from the time that you

start pulling the stump with the truck until the time that the

stump comes out from the ground.

Wout =

Incorrect

Tries 16/99

Also, nd the power delivered to the stump at half the time

from when the truck starts to pull to when the stump breaks

free (tout=2).

Pout =

Tries 0/99

Once the stump breaks free, all horizontal forces on the stump

except the force from the cable are negligible for a time, and

the force from the wire as a function of position becomes:

Fws(x) = Fout

8 [1+7e��cx] where Fout is the same as above, c is

a constant, and x is the distance that the stump has traveled.

After you pull out the stump, you drag it a horizontal distance

x1 with the truck. Find the work done on the stump by the

winch from when it started moving until it reaches a distance

x1. The stump does not come o the ground during this

time, and the angle doesn't change. Use the following values

in your calculation: c = 7.0 m��1

x1 = 3.9 m

= 51.0 degrees W1 =

Tries 0/99

Find the speed of the stump when it is at position x1. Re-

member, all horizontal forces on the stump are negligible ex-

cept the force from the cable until after the stump has traveled

past x1.

v1 =

Tries 0/99

Homework 5-1

What is the power being delivered to the stump by the cable

when it is at the position x1?

P1 =

Tries 0/99

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##### Solution Summary

Solution gives all mathematical steps.

##### Solution Preview

1. Force on the block F = F(t)Cos(90-51) = 0.777 F(t)

The block will come out when the force F(t) reaches Fout = 17000 N

We will write, 17000 N = 0.777 * Fo Exp(bt)

Or, Exp(bt) = 17000/(0.777*20) where b = 4.1/sec

exp(4.1 t) = 1093.95

or, 4.1 t = ln(1093.95)

===> t = 6.997/4.1 = 1.7 Sec ---Answer

2. Workdone = force x displacement

Also work done = change in Kinetic enegy of the stump

If we know the force as a function of time, then we can get the velocity of the mass after a time t from Newton's law.

m dv/dt = F(t)

dv = (1/m) F(t)dt

V = integral from time t=o to t=1.7 of this value

= (1/m) int(0 to 1.7) 0.777 ...

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