When a boat paddle is submerged in water and moved to propel a boat, several forces come into play. The force exerted by the paddle on the water is equal to the amount of water displaced by the paddle and the acceleration of the water. This force results in an equal and opposite reaction force on the paddle from the water, which propels the boat forward. The force exerted by the paddle depends on various factors, including the speed and direction of the boat, the size and shape of the paddle, and the strength of the person paddling. To calculate the force, one must consider the mass of water displaced per second, the velocity of the water, and the paddle's surface area. Additionally, factors such as water pressure, water density, and the paddle's angle in the water also influence the force exerted by the paddle.

Characteristics | Values |
---|---|

Factors affecting force exerted by a boat paddle | The speed and direction of the river's current, the size and shape of the paddle, the weight and strength of the person holding the paddle, the type and materials of the paddle, and external forces such as wind or waves |

Newton's third law and surface area of paddles | A larger surface area of a paddle allows for more force to be applied to the water, resulting in the paddle travelling more quickly through the water |

Buoyant force exerted by the water on the boat | Weight of the water displaced (density of water is 1000 kg/m^3) multiplied by the volume of water displaced (length x width x height of the boat) |

Boat acceleration | Net boat force (the sum of all individual force vectors acting on the boat) multiplied by the mass of the boat |

Measuring force of a single paddle stroke | Strain gauges on the paddle to measure its bending, lasers to measure flex in the paddle, water displacement, accelerometers attached to the boat, video analysis of the paddling technique, measuring boat acceleration |

## What You'll Learn

**The effect of paddle size on exerted force**

The exerted force on a boat paddle is influenced by several factors, including the size and shape of the paddle, the speed and direction of the river's current, and the strength of the person paddling. Let's delve into the effect of paddle size on the exerted force in the following paragraphs:

The size of a boat paddle plays a significant role in determining the force exerted by the paddler and the resulting motion of the boat. A larger paddle with a greater surface area will encounter more resistance from the water, requiring the paddler to apply more force to propel the boat forward. This increased resistance is advantageous for generating higher speeds, as the larger paddle allows for more force to be applied to the water, resulting in a quicker movement through the water. This is in accordance with Newton's third law, which states that for every action, there is an equal and opposite reaction.

However, a larger paddle also means that the paddler will need to put in more effort. The increased resistance from the water will demand a stronger force to be applied, and the paddler might need to increase their paddling strokes to maintain the same speed. This can lead to higher energy expenditure and increased fatigue for the paddler. Therefore, while a larger paddle can generate more force and speed, it also requires more strength and energy to use.

On the other hand, a smaller paddle with a reduced surface area will encounter less resistance from the water. This means that the paddler will need to apply less force to move the paddle through the water. As a result, the boat may not achieve the same level of speed and acceleration as it would with a larger paddle. However, a smaller paddle can be advantageous in situations where maneuverability and energy conservation are more important than speed.

The shape of the paddle also influences the exerted force. Curved paddles, for example, can create more propulsion force compared to flat paddles, up to a certain angle of curvature. Additionally, the optimal paddle size for proficient adult swimmers is said to be between 210 and 358 square centimetres, according to studies. This size allows for a balance between propulsion force and the force exerted on the swimmer's body.

In conclusion, the size of a boat paddle directly impacts the force exerted by the paddler and the resulting motion of the boat. Larger paddles generate more force and speed but require more strength, while smaller paddles are easier to use but may not provide the same level of propulsion. The shape of the paddle also plays a role, with curved paddles often providing more propulsion than flat ones. Ultimately, the ideal paddle size depends on factors such as the strength and technique of the paddler, as well as the specific requirements of speed, maneuverability, and energy conservation.

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**The role of water resistance**

Water resistance plays a crucial role in understanding the force exerted by a boat paddle. When a paddle is submerged in a river, the water exerts a force on the paddle, opposing its motion. This force is known as drag force or water resistance, and it depends on factors such as the velocity and density of the water, the angle of the paddle, and the shape and size of the paddle's surface area.

The water resistance on the paddle can be calculated by determining the mass per second that collides with the paddle. This can be found using the water's velocity and density. By multiplying the density of water by the velocity and the sin of the angle between the water and the paddle, we can find the mass per second. This value represents the rate at which water collides with the paddle, influencing the force exerted on it.

The shape and size of the paddle's surface area also come into play. A larger surface area increases the resistance from the water, resulting in a greater force exerted on the paddle. This is because a larger area allows for a greater amount of water to be pushed, creating more resistance and, consequently, a higher force. Additionally, the angle at which the paddle is held in the water affects the force. The force exerted by the water is proportional to the sine of the angle between the paddle and the direction of motion.

Furthermore, water resistance is a crucial factor in boat design and hull optimisation. The hull is the part of the boat that comes into direct contact with the water, and reducing resistance on the hull can significantly improve the boat's efficiency. One method to achieve this is through air lubrication, where a layer of air bubbles is applied to the hull, reducing frictional resistance. Another approach is hull form optimisation, which involves modifying the design of the forward region of the ship, including the bulb design, forward shoulder, and waterline entrance, to reduce wave-making resistance.

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**The impact of velocity and density**

The velocity and density of the water play a crucial role in determining the force exerted by a boat paddle.

Firstly, let's consider the impact of velocity. When a paddle is submerged in a river, the force exerted on it is influenced by the speed and direction of the river's current. As the current creates resistance on the paddle, the force increases with higher velocities. This resistance makes it more challenging to move the paddle through the water, and the force will vary depending on the angle between the paddle and the current.

Now, let's discuss the impact of density. The mass of water that collides with the paddle per second is determined by the water's velocity and density. By calculating the mass per second and finding its rate of change of momentum, we can determine the force exerted on the paddle. This calculation takes into account the density of the water and how it affects the amount of mass colliding with the paddle.

Additionally, the shape and size of the paddle also come into play. A larger surface area of the paddle allows for more force to be applied to the water, resulting in a quicker movement through the water. This is because a larger paddle has more resistance and can displace more water, creating a greater reaction force.

In conclusion, the velocity and density of the water are crucial factors in calculating the force exerted by a boat paddle. The speed and direction of the current impact the force directly, while the density influences the mass of water colliding with the paddle. The size and shape of the paddle also contribute to the overall force exerted, with larger paddles providing more resistance and faster movement.

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**Newton's third law and its application**

Newton's third law of motion is one of the fundamental principles in physics, governing the interactions of forces in our universe. This law, also known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. In other words, when two objects interact, they exert forces on each other that are equal in magnitude but opposite in direction.

Now, let's apply this law to the scenario of a boat paddle. When a boatman rows a boat, they push the water backward with their paddle (action force). In response, the water exerts an equal and opposite force on the paddle and the boat, propelling them forward (reaction force). This is a clear demonstration of Newton's third law in action.

The size and shape of the paddle also come into play here. A larger paddle will have a greater surface area, resulting in more resistance from the water and a greater force exerted on the paddle. This, in turn, affects the force required by the boatman to push the paddle through the water. Additionally, the speed and direction of the river's current play a role in the force exerted on the paddle. Faster-moving water will exert greater resistance, resulting in a higher force on the paddle.

Understanding Newton's third law is crucial for optimising techniques in rowing and paddling. By applying this law, paddlers can choose the right equipment and improve their efficiency. For instance, using a larger paddle with a greater surface area can increase the force exerted on the water, resulting in more effective paddling and faster movement through the water.

In conclusion, Newton's third law of motion provides valuable insights into the forces exerted by and upon a boat paddle. By comprehending this law, we can enhance our understanding of the physical world and make practical applications in various fields, including sports and engineering.

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**Buoyant force and weight displacement**

For a boat to float, the buoyant force must be greater than or equal to the weight of the boat and its contents. This is achieved by ensuring the boat displaces an equal weight of water. For example, a 50kg kayaker and boat would displace 50kg of water, while an 80kg kayaker and boat would displace 80kg of water. This balance of forces allows the kayaker to remain afloat.

The shape of the boat also plays a crucial role in weight displacement. The underwater hull volume must be designed to displace a weight of water that will support the entire boat. The shape and size of the hull determine how effectively the boat can move through the water, as it must displace enough water to counter the downward force of gravity acting on the boat and its contents.

Additionally, the distribution of weight within the boat can impact its stability. By manipulating the shape of the kayak's cross-section and the height of the seat, designers can control the boat's stability. A higher centre of gravity can make the kayak unstable, while a lower centre of gravity can improve stability.

In summary, the buoyant force experienced by a boat is directly related to the weight of the fluid it displaces. Boat designers must carefully consider the hull volume and shape to ensure effective weight displacement and maintain the boat's buoyancy and stability.

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**Frequently asked questions**

The force exerted by a boat paddle is influenced by several factors, including the speed and direction of the water current, the size and shape of the paddle, and the strength of the person paddling. Additionally, the weight and type of material used for the paddle can also impact the force exerted.

A larger surface area on the paddle allows for more force to be applied to the water, resulting in increased resistance from the water and a greater forward reaction force on the boat. A smaller paddle, on the other hand, may require more strokes to achieve the same force.

The speed and direction of the current create resistance on the paddle. In faster-moving water, the force exerted on the paddle will be greater due to increased resistance. The direction of the current also plays a role, as paddling against the current will require more force than paddling with it.

There are several methods to measure the force exerted by a boat paddle. One way is to use strain gauges attached to the paddle to measure its bending during a stroke. Another method is to use a tether connected to the boat and a device that measures pulling force. Additionally, accelerometers and video analysis can be used to study the movement of the boat and paddle.