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at a county fair truck pull, two pickup trucks are attached to the back end of a monster truck as illustrated in the figure. One of the pickups pulls with a force of 3000 pounds and the other pulls with a force of 2500 pounds with an angle of 60 degrees between them. With how much force must the monster truck pull in order to remain unmoved? (find the resultant of the two trucks)


vector problem

Verified Answer :

Suppose truck A is the one who is pulling with 3000 lbs and truck B the one pulling with 2500 lbs. Suppose that the force of truck A is aligned along the x-axis and the force of truck B is aligned in the first quadrant. Now lets solve the components of the resultant force.

Rx = 3000 + 2500 cos(60) = 4250Ry = 2500 sin(60) = 2165.064R = sqrt(Rx^2 + Ry^2) = 4770 lbs.

Therefore, the monster truck has to pull 4770 lbs.


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Answer:

Monster truck should apply 4770 pounds to make system stable or unmoved.

Step-by-step explanation:

In the figure attached Pickup truck truck 1 is pulling up with a force of 25000 pounds and Truck 2 is pulling up with a force of 3000 lb.

These force are acting on a angle of 60°.

We have to find the measure of pull applied by monster truck to make the system unmoved or stable.

Now from the figure we can easily say the if monster truck pulls with a force which is equal and opposite to the resultant of two forces applied by pick up trucks then system will remain unmoved.

Since R² = 2500² + 3000² + 2(2500)(3000)cos60° (Resultant vector R²= a² + b² + 2ab cos∅)

\(R^{2}= 625(10)^{4} +900(10)^{4}+2(25)(30)(10)^{4}(\frac{1}{2})\)

\(R^{2}=1525(10)^{4}+750(10)^{4}=2275(10)^{4}\)

\(R=\sqrt{2275(10)^{4}}\)

\(R=47.6969(10)^{2}=4769.69\)

Therefore, Monster truck should apply force of 4770 pounds.

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