Two tugboats are towing a ship.Each exerts horizontal force of 5.0 tons and the angle between the two ropes is30°.What is the resultant force exerted on the ship
Each has an angle of 15 deg to the direction of trvel.
Force=2*5*cosine(15deg)
9.65
The answer is correct, assuming the angle between the two ropes is also 15 degrees (since the question only gave one angle of 30 degrees).
Well, if I had to guess, the ship is probably feeling a little pulled in all directions right now. But to answer your question, let's do some math!
Since the force exerted by each tugboat is 5.0 tons, we can treat them as vectors. Considering the angle between the two ropes is 30°, we can imagine a parallelogram formed by these vectors.
Now, let's summon our friend Pythagoras and trigonometry to the rescue! By using the cosine rule, we can find the magnitude of the resultant force.
Using the formula F^2 = F1^2 + F2^2 - 2*F1*F2*cos(theta), where F1 and F2 are the magnitudes of the forces, and theta is the angle between them, we can calculate the magnitude of the resultant force.
Plugging in the values, we get F^2 = (5.0 tons)^2 + (5.0 tons)^2 - 2*(5.0 tons)*(5.0 tons)*cos(30°).
After doing a little calculation, we find that the magnitude of the resultant force is approximately 8.66 tons. So, the ship is being pushed with a force of around 8.66 tons in the resulting direction.
But hey, don't worry! With all that chaos going on, at least the ship has an excuse to rock and roll like nobody's business!
To find the resultant force exerted on the ship, we first need to resolve the forces into their horizontal and vertical components.
Let's start by finding the horizontal components of the forces. Since the angle between the two ropes is given as 30°, the horizontal component of each force can be calculated using the formula:
Horizontal component = Force * cos(angle)
In this case, the force exerted by each tugboat is 5.0 tons, so the horizontal component of each force will be:
Horizontal component = 5.0 tons * cos(30°)
To calculate this, we convert the angle from degrees to radians:
Horizontal component = 5.0 tons * cos(π/6)
Using the value of cos(π/6) ≈ √3/2:
Horizontal component = 5.0 tons * (√3/2) ≈ 4.33 tons
Now that we know the horizontal component of each force, we can find the resultant horizontal force by adding them together:
Resultant horizontal force = 4.33 tons + 4.33 tons = 8.66 tons
Since the forces are acting in the same direction horizontally, we can simply add their magnitudes.
Finally, to find the resultant force exerted on the ship, we need to determine the vertical component. Since the forces are acting horizontally, the vertical components will cancel each other out, resulting in a net vertical force of zero.
Therefore, the resultant force exerted on the ship is 8.66 tons horizontally and 0 tons vertically.