# Physics

posted by .

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.

• Physics -

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)>

• Physics -

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.

• Physics -

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.

c^2=a^2+b^2-2ab*cos120
= 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.

## Similar Questions

1. ### Physics

A 4 kg block resting on a horizontal surface is attached to an 8 kg block that hangs freely by a cord passing over a frictionless pulley. The coefficient of kinetic friction between the block and the horizontal surface is 0.4. Find …
2. ### Physics

A student pulls on a rope attached to a box of books with a mass of 35.0 kg and moves the box up a ramp at 12 degrees with the horizontal. If the box starts from rest at the bottom of the ramp and is pulled at an angle 25.0 degrees …
3. ### Physics

Two dogs are pulling on opposite ends of a bone. One dog pulls to the right with a force of 50N while the other pulls to the left with a force of 40N. Are the forces balanced or unbalanced?
4. ### Physics

The helicopter view in the figure below shows two people pulling on a stubborn mule. Assume that F1 is 130 N, and F2 is 65 N. The forces are measured in units of newtons (N). (a) Find the single force that is equivalent to the two …
5. ### Physics

A 1,200-kg car is pulling a 305-kg trailer. Together, the car and trailer have an acceleration of 2.00 m/s2 in the positive x-direction. Neglecting frictional forces on the trailer, determine the following. (Indicate the direction …
6. ### physics

A box containing supplies is vertically lowered at constant speed by a rope from a hovering helicopter. Consider the following forces that arise in this situation: force 1: the force of the earth pulling on the box force 2: the tension …
7. ### physics

Two crewmen pull a boat through a lock, as shown in Figure 5-25. One crewman pulls with a force of F1 = 155 N at an angle of θ = 32° relative to the forward direction of the raft. The second crewman, on the opposite side of the …
8. ### Physics

Assume the sleigh and horse pulling it are on a level, horizontal surface. Given: mass of sleigh 475 kg / force of horse pulling sleigh 1.5×10^5 / coef. of kinetic friction .15 / coef. of static friction .20 a.) What is the normal …
9. ### 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 backward, …
10. ### PHYSICS

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?

More Similar Questions