Supertank has engine exerting a 75x10 cube N, Force against water drag at 40x10cubeN, Calculate tensions in tugs cable, Supertank is 1piont5x10eight kg
30 degrees vertical pull, Acceleration 2x10negative3 m/s?
To calculate the tensions in the tug's cable, we need to consider the forces acting on the supertank and use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration.
Let's break down the forces acting on the supertank:
1. Engine Force: The engine exerts a force of 75 × 10^3 N (newtons) against the water drag.
2. Water Drag: The water drag provides a resistance force of 40 × 10^3 N in the opposite direction of the supertank's motion.
Now, let's calculate the net force acting on the supertank:
Net force = Engine Force - Water Drag
= 75 × 10^3 N - 40 × 10^3 N
= 35 × 10^3 N
Next, we can calculate the acceleration of the supertank using its mass and the net force:
Mass of supertank = 1.5 × 10^8 kg
Acceleration = Net force / Mass
= (35 × 10^3 N) / (1.5 × 10^8 kg)
= 2 × 10^-3 m/s^2
Now, let's calculate the tension in the tug's cable. Since the supertank is being pulled vertically at a 30-degree angle, we need to consider the vertical component of the tension.
Tension = Mass × Acceleration + Weight × sin(theta)
Weight = Mass × acceleration due to gravity
= 1.5 × 10^8 kg × 9.8 m/s^2
= 1.47 × 10^9 N
θ = 30 degrees
sin(30 degrees) = 0.5
Tension = Mass × Acceleration + Weight × sin(theta)
= 1.5 × 10^8 kg × 2 × 10^-3 m/s^2 + 1.47 × 10^9 N × 0.5
= 3 × 10^5 N + 7.35 × 10^8 N
= 7.35 × 10^8 N + 3 × 10^5 N
= 7.35 × 10^8 N + 0.3 × 10^6 N
= 7.38 × 10^8 N
Therefore, the tension in the tug's cable is approximately 7.38 × 10^8 N.