A tugboat is towing a ship with a tow rope as shown below . $\qquad$
titsite

Mass of tugboat $=20 imes 10^{4} \mathrm{~kg} \quad$ Mass of ship $=100 imes 10^{4} \mathrm{~kg}$
The tugboat exerts a constant force of $9.0 imes 10^{4} \mathrm{~N}$ on the tow rope. The water resistance on the ship as a function of speed is shown in Figure 2.
aro labom tisigec $\square$
(1) What is the acceleration of the ship when the tugboat and ship are travelling at $2.0 \mathrm{~m} \mathrm{~s}^{-1}$ ? You must show your working.
(2)After a time, the tugboat and ship are travelling at a constant speed. What is this constant speed? $\square$

Question

A tugboat is towing a ship with a tow rope as shown below . $\qquad$
titsite

Mass of tugboat $=20 	imes 10^{4} \mathrm{~kg} \quad$ Mass of ship $=100 	imes 10^{4} \mathrm{~kg}$
The tugboat exerts a constant force of $9.0 	imes 10^{4} \mathrm{~N}$ on the tow rope. The water resistance on the ship as a function of speed is shown in Figure 2.
aro labom tisigec $\square$
(1) What is the acceleration of the ship when the tugboat and ship are travelling at $2.0 \mathrm{~m} \mathrm{~s}^{-1}$ ? You must show your working.
(2)After a time, the tugboat and ship are travelling at a constant speed. What is this constant speed? $\square$

Accepted Answer

∻Solution∻ ‖ a ⋮ To find the acceleration of the ship when the tugboat and ship are traveling at $2.0 \, \mathrm{m/s}$, we first need to calculate the net force acting on the ship. The tugboat exerts a constant force of $F_{tug} = 9.0 imes 10^{4} \, \mathrm{N}$. The water resistance on the ship at this speed can be determined from the graph, which we assume gives a value of $F_{resistance}$. The net force is then given by: $$F_{net} = F_{tug} - F_{resistance}$$. Using Newton's Second Law, we can find the acceleration: $$a = \frac{F_{net}}{m_{ship}}$$, where $m_{ship} = 100 imes 10^{4} \, \mathrm{kg}$. ‖ ‖ b ⋮ After determining the net force and calculating the acceleration, we can find the constant speed of the tugboat and ship after some time. At constant speed, the net force is zero, meaning the driving force exerted by the tugboat equals the total water resistance acting on the ship. Thus, we can set up the equation: $$F_{tug} = F_{resistance}$$. Solving for the speed at which this balance occurs will give us the constant speed. ‖ ∻Answer∻ ⚹ [Insert final answer here] ⚹ ∻Key Concept∻ ⚹ Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation: $$F = ma$$ (Net force equals mass times acceleration). The concept of net force and resistance is crucial in determining acceleration and constant speed. ⚹ ∻Explanation∻ ⚹ The acceleration is calculated by finding the net force acting on the ship and dividing it by the mass of the ship. The constant speed is found by equating the tugboat's force to the water resistance, indicating no net force at that speed. ⚹

Sia