A rope connects boat A to boat B. Boat A starts from rest and accelerates to a speed of 9.5 m/s in a time t = 47 s. The mass of boat B is 540 kg. Assuming a constant frictional force of 230 N acts on boat B, what is the magnitude of the tension in the rope that connects the boats during the time that boat A is accelerating?

Answer: 339.148N

Explanation:

Data

Time (t) = 47s

U = 0m/s

V = 9.5m/s

Mass of B = 540kg

Frictional force on B = 230N

Both boats are connected so if A moves, B moves too.

Acceleration of boat A = ?

Using equation of motion,

V = u + at

9.5 = 0 + a*47

a = 9.5 / 47

a = 0.2021 m/s²

The force required to accelerate boat B since it's the same force moving both boats = ?

F = Mass * acceleration

F = 540 * 0.2021 = 109.14N

A frictional force of 230N exists on boat B

Total force (Tension) = frictional force + normal force = (109.15 + 230) N = 339.148N