Two people are pulling a boat through the water as in the figure below. Each exerts a force of 600 N directed at a è = 45.0° angle relative to the forward motion of the boat. If the boat moves with constant velocity, find the resistive force exerted by the water on the boat.
each is pulling with a forward component of 600cos45
Resistive force then is 1200cos45
To find the resistive force exerted by the water on the boat, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, since the boat is moving with constant velocity, its acceleration is zero. Therefore, the net force acting on the boat must be zero as well.
In the figure given, we have two forces acting on the boat - the forces exerted by the two people pulling the boat. Each person exerts a force of 600 N at an angle of 45.0° relative to the forward motion of the boat.
To calculate the net force in the horizontal direction (which is the direction of the boat's forward motion), we need to resolve the forces into their horizontal and vertical components. The horizontal component of each force can be found by multiplying the force magnitude by the cosine of the angle, while the vertical component can be found by multiplying the force magnitude by the sine of the angle.
Given that the angle is 45.0°, the horizontal component of each force is:
F_horizontal = 600 N * cos(45.0°)
And the vertical component of each force is:
F_vertical = 600 N * sin(45.0°)
Since the boat is moving with constant velocity, the net force in the horizontal direction (F_horizontal_net) must be zero. This means that the sum of the horizontal components of the forces exerted by the two people must also be zero.
F_horizontal_net = F_horizontal_1 + F_horizontal_2
0 = 600 N * cos(45.0°) + 600 N * cos(45.0°)
Solving this equation, we can find the value of the horizontal components of the forces exerted by each person.
Now, let's consider the vertical components of the forces. Since the boat is not sinking or rising, the net force in the vertical direction (F_vertical_net) must also be zero. This means that the sum of the vertical components of the forces exerted by the two people must also be zero.
F_vertical_net = F_vertical_1 + F_vertical_2 + F_resistive
0 = 600 N * sin(45.0°) + 600 N * sin(45.0°) + F_resistive
Solving this equation, we can find the value of the resistive force exerted by the water on the boat (F_resistive).