Physics: force and motion

code PLUS

2011-11-19 4:25 am

Two horses A and B pull a stump with two ropes. The pulling forces Fa and Fb exerted by horses A and B on the stump are 1500 N and 1200 N respectively. The two forces make an angle of 75° .

Find the resultant force acting on the stump.

回答 (1)

天同

2011-11-19 5:10 am

✔ 最佳答案

Let a be the angle between force Fa (the 1500 N force) and the direction of motion of the stump.
Hence, angle between force Fb and direction of stump motion is (75-a)

Consider forces in direction perpendicular to the direction of motion of the stump, we have,

1500.sin(a) = 1200sin(75-a)
i.e. 5sin(a) = 4[sin(75).cos(a) - cos(75).sin(a)]
5.sin(a) = 3.864.cos(a) - 1.035sin(a)
6.035.sin(a) = 3.864.cos(a)
tan(a) = 0.6403
a = 32.63 degrees

Therefore, the resultant force acting on the stump
= [1500.cos(32.63) + 1200.cos(75-32.63)] N
= 2150 N

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