The drawing shows a boat being pulled by two locomotives through a canal of length 2.50 km. The tension in each cable is 5.00 103 N, and è = 19.0°. What is the net work done on the boat by the two locomotives?
work= force * distance cosine Theta
= 2*5000*2500*cos19/2
I assume the angle between the ropes is 19deg.
Well, it sounds like these locomotives are really going off the rails to pull a boat through a canal! But let's calculate the net work done on the boat anyway.
To find the net work done on the boat, we need to consider the force applied and the displacement of the boat.
The force applied by each locomotive is the tension in each cable, which is 5.00 x 10^3 N. So, the total force applied is 2 * 5.00 x 10^3 N = 10.00 x 10^3 N.
The displacement of the boat through the canal is 2.50 km = 2.50 x 10^3 m.
Now, to calculate the net work done, we can use the formula:
Net work = Force * Displacement * cos(θ)
Where θ is the angle between the force vector and the displacement vector.
In this case, θ = 19.0°, and cos(19.0°) ≈ 0.943.
So, the net work done on the boat is:
Net work = 10.00 x 10^3 N * 2.50 x 10^3 m * 0.943 ≈ 23.57 x 10^9 J
Wow, that's a lot of work! It looks like these locomotives are really putting their steam into pulling that boat through the canal. Keep up the good work, locomotives!
To find the net work done on the boat by the two locomotives, we need to calculate the work done by each locomotive and then add them together.
The work done by a force can be calculated using the formula:
Work = Force * Distance * cos(angle)
For each locomotive, the force is the tension in the cable (5.00 * 10^3 N), the distance is the length of the canal (2.50 km or 2500 m), and the angle is the angle between the force and the direction of motion (19.0°).
Calculating the work done by each locomotive:
Work1 = 5.00 * 10^3 N * 2500 m * cos(19.0°)
Work2 = 5.00 * 10^3 N * 2500 m * cos(19.0°)
Adding the work done by each locomotive gives us the net work done on the boat:
Net Work = Work1 + Work2
To find the net work done on the boat by the two locomotives, we can use the formula for work done:
Work = Force * Displacement * cos(theta)
In this case, the force is the tension in each cable, which is given as 5.00 x 10^3 N. The displacement is the length of the canal, which is given as 2.50 km. However, before we can calculate the work, we need to convert the displacement from km to meters since the force is given in newtons.
1 km = 1000 m
Therefore, the displacement is 2.50 km * 1000 m/km = 2500 m.
Now we can calculate the work done on the boat:
Work = (5.00 x 10^3 N) * (2500 m) * cos(19.0°)
To find the value of cos(19.0°), we can use a calculator. After finding the value, substitute it into the equation to calculate the work done on the boat.