Forces 2 dimensions: How far have the tugboats moved the log

  • #1

Homework Statement


Two tugboats are pulling on a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s?
upload_2016-5-6_20-36-9.png


Homework Equations


c2 = a2 + b2 - 2abcosC

c = (a2 + b2- 2abcosC)1/2

upload_2016-5-4_15-22-57-png.100276.png


upload_2016-5-6_20-50-52.png




The Attempt at a Solution


[/B]
c2 = a2 + b2 - 2abcosC

c = (a2 + b2- 2abcosC)1/2

c = [(400 N)2 + (800 N)2 - 2 (400 N) x (800 N) cos 150°]1/2

c= 1164 N

sinβ/800 N = sin 150°/ 1164 N

β = 20°

(To determine the angle for Fnet, subtract 10° from 20°, which equals 10°, as this results in the angle needed to describe the direction for Fnet.)

Fnet = 1164 N [W 10° N]

a = 1164 N [W 10° N] / 250 kg

= 4.66 m/s2 [W 10° N]

Δd = ½ 4.66 m/s2[W 10° N] x (10 s)2

Δd = 233 m [W 10° N]

The tugboats have moved the log 233 m [W 10° N] after 10 seconds.

Is this correct?
 

Answers and Replies

  • #2
haruspex
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Homework Statement


Two tugboats are pulling on a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s?
View attachment 100372

Homework Equations


c2 = a2 + b2 - 2abcosC

c = (a2 + b2- 2abcosC)1/2

upload_2016-5-4_15-22-57-png.100276.png


View attachment 100373



The Attempt at a Solution


[/B]
c2 = a2 + b2 - 2abcosC

c = (a2 + b2- 2abcosC)1/2

c = [(400 N)2 + (800 N)2 - 2 (400 N) x (800 N) cos 150°]1/2

c= 1164 N

sinβ/800 N = sin 150°/ 1164 N

β = 20°

(To determine the angle for Fnet, subtract 10° from 20°, which equals 10°, as this results in the angle needed to describe the direction for Fnet.)

Fnet = 1164 N [W 10° N]

a = 1164 N [W 10° N] / 250 kg

= 4.66 m/s2 [W 10° N]

Δd = ½ 4.66 m/s2[W 10° N] x (10 s)2

Δd = 233 m [W 10° N]

The tugboats have moved the log 233 m [W 10° N] after 10 seconds.

Is this correct?
Looks good.
 
  • #3
Ok thanks :)
 

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