Two tugboats are pulling a freighter. Find the net force and direction of the acceleration for the following cases. Assume that each tugboat pulls with a force of 1.2 x 10^5 N. Assume no resistive force at this time.
a) Tugboat 1 pulls in a direction given by [N 60 degrees E] and tugboat 2 pulls in a direction given by [S 60 degrees E].

The answer says: Fnet=(1.2 x 10^5 cos 30 degrees ) x2
=2.1 x 10^5 N [E]

but I don't know know they got that.
I used the cosine law with contained angle 60 degrees, but my answer was different from the previous one.

Thanks in advance!

  1. 👍
  2. 👎
  3. 👁
  1. look at the angles, each is pulling to the side of the forward direction by 30 deg.

    The component of each rope to the side is equal and opposite, so they add to zero side force.

    Now the forward force on each rope is Tension*cos30. There are two of those.

    2*Tension*cos30deg is the net force, and of course it is in the East direction. acceleration is this force divided by the mass of the tug (neglecting friction)>

    1. 👍
    2. 👎
  2. How come we don't use the cosine law? In an example, they used the cosine law to find Fnet:

    A person of mass 70 kg is sitting on a 20 kg toboggan. If the two people are pulling her with two different ropes, find the person's acceleration. The force of person 1 is 50 N [ E 40 degrees N], and the force of person 2 is 60 N [E 25 degrees S] as seen from the top.

    In this example, they used the cosine law with contained angle 115 degrees to find Fnet.

    1. 👍
    2. 👎
  3. You can use the law of cosines here, but it is much more complicated. Two sides a,b are the vectors (head to tail), and c is the unknown side. The angle between the vectors is 180-60=120

    draw a triangle to prove that.

    = 2*tension^2( 1-cos120)
    =2 tension^2 (1+cos60)
    = 2 tension^2(1+1/2)=3 tension^2
    c= tension*sqrt3 which is the same as above 2*tension*cos30.

    Now, with the law of cosines, you have then to use the law of sines to get the angle for the resultant.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    The curves on a race track are banked to make it easier for cars to go around the curves at high speed. Draw a free-body diagram of a car on a banked curve. From the motion diagram, find the direction of the acceleration. The

  2. physics

    A negative charge Q1 = -20.0 mC is located at a point X1 = -2.00 m, a positive charge Q2 = 10.0 mC is located at a point X2 = 3.00 m and a positive charge Q3 = 30.0 mC is located at a point X3 = 9.0 m.a. Draw free body diagrams

  3. Physics (Newton's laws)

    Two blocks of mass 3.50 kg and 8.00 kg are connected by a massless string that passes over a frictionless pulley. The inclines are frictionless and the angles with the horizontal is 35 degrees. Find a) the magnitute of the

  4. Physics

    A crate is pulled right with a force of 82.0N to the left wtih a force of 115N upward with a force of 565N and downward with a force of 236N Fine the net external force in the X direction Find the net external force in the y

  1. physics

    If the 1 kg standard body has an acceleration of 2.00 m/s2 at 20.0° to the positive direction of an x axis, what are (a) the x component and (b) the y component of the net force acting on the body, and (c) what is the net force

  2. Science in motion pHY 102

    Find the net force produced by a 30-N force and a 20-N force in each of these cases: (a) Both forces act in the same direction. The net force produced by 30-N force is 60-N The net force produced by 20-N force is 40=N Applied


    On vacation, your 1400-kg car pulls a 520-kg trailer away from a stoplight with an acceleration of 2.00 m/s2 . A: What is the net force exerted by the car on the trailer? Assume that the positive x axis is directed toward the

  4. Physics

    Newton's second law states that if an object has zero acceleration, the net force acting on it is zero. My question is if you have an object at constant acceleration moving downward is there a net force being applied to it? Does

  1. physics

    a 1250 kg car is pulling a 325 kb trailer. The car and trailer have an acceleration of 2,15m/sec2 together. Determine the net force on the ca-trailer combination. What is the net force on the railer?

  2. Physical Science

    Two tugboats are towing a ship. each exerts a horizontal force of 5 tons and the angle between their tow ropes is 90. what net force is exerted on the ship?

  3. Physics

    I was wondering if my answers are correct. 1. A 50kg person is taking a ride on an elevator travelling up at a steady speed of 2.5m/s. Find the time fo the elevator trip if the elevator does 4900 J of work on the person. My

  4. science

    Three dogs—Ed, Max, and Marcie—are pulling a dogsled along a patch of ice. Ed pulls with a force of 115 N; Max pulls with a force of 62 N; and Marcie pulls with a force of 90 N. If there are no forces pulling the sled

You can view more similar questions or ask a new question.