GOAL Apply Newton\'s second law in a two-dimensional problem. PROBLEM Two horses
ID: 2134011 • Letter: G
Question
GOAL Apply Newton's second law in a two-dimensional problem. PROBLEM Two horses are pulling a barge with mass2.00 times 103 kg along a canal, as shown in the figure. The cable connected to the first horse makes an angle of ?1 = 30.0degree with respect to the direction of the canal, while the cable connected to the second horse makes an angle of ?2 = ?45.0degree. Find the initial acceleration of the barge, starting at rest, if each horse exerts a force of magnitude 6.00 times 102 N on the barge. Ignore forces of resistance on the barge.Explanation / Answer
Horse 1
Fx = 600(cos30) = 519.6 N
Fy = 600(sin 30) = 300 N
Horse 2
Fx = (600)(cos 45) = 424.3 N
Fy = (600)(cos 45) = -424.3 N
Net x = 519.6+ 424.3 = 943.9 (right)
Net y = 424.3 - 300 = -124.3 (down)
Net force = sqrt[(943.9)^2 + (124.3)^2]
Net force = 952 N
Fx = max
943.9 = 2000a
ax = .472 m/s^2
Fy = may
-124.3 = 2000a
a = -.0622 m/s^2 (Negative means downward)
F = ma
952 = 2000(a)
a = .476 m/s^2
The angle is found from the tangent formula
tan(angle) = 124.3/943.9
angle = -7.50 degrees
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True, the magnitude of the acceleration of an object is determined by the magnitudes of the forces acting on it.
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Horse 1
Fx = 593(cos30) = 513.6 N
Fy = 593(sin 30) = 296.5 N
Horse 2
Fx = (593)(cos 45) = 419.3 N
Fy = (593)(cos 45) = -419.3 N
Net x = 513.6+ 419.3 = 932.9 (right)
Net y = 419.3 - 296.5 = -122.8 (down)
Net force = sqrt[(932.9)^2 + (122.8)^2]
Net force = 941 N
F = ma
941 = 1870(a)
a = .503 m/s^2
The angle is found from the tangent formula
tan(angle) = 122.8/932.9
angle = -7.50 degrees
Next Question
Horse 1
Fx = 593(cos41.2) = 446.2 N
Fy = 593(sin 41.2) = 390.6 N
Horse 2
Fx = (593)(cos 16.3) = 569.2 N
Fy = (593)(sin 16.3) = -166.4 N
Net x = 446.2 + 569.2 = 1015.4 (right)
Net y = 390.6 - 166.4 = 224.2 (up)
Net force = sqrt[(1015.4)^2 + (224.2)^2]
Net force = 1040 N
F = ma
1040 = 1870(a)
a = .556 m/s^2
The angle is found from the tangent formula
tan(angle) = 224.2/1015.4
angle = 12.5 degrees
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