A 1.31 g samara -- the winged fruit of a maple tree -- falls toward the ground with a constant speed of 1.0 m/s (Figure 5-29).
I understand that acceleration equals zero, but I don't understand how to find the upward force need to keep the fruit at 1.0 m/s. Is kinematics necessary in this question?
If there is no acceleration, as is the case here, there must be an upward force that balances the weight, so that the net force is zero.
I assume you know how to calculate the weight when you know the mass.
The 1 m/s speed will not make a difference in your answer. It is what is called the termimal speed.
.0119 N
To find the upward force needed to keep the fruit at a constant speed of 1.0 m/s, we need to consider the forces acting on the samara.
Since the fruit is falling with a constant speed, the net force acting on it must be zero. This means that the gravitational force pulling the samara downward is balanced by an opposite and equal force pushing it upward. This upward force is provided by air resistance.
The force of air resistance depends on several factors, including the shape and size of the object. In this case, since the samara is wing-shaped, it will experience a drag force due to air resistance.
Kinematics is not necessary to find the upward force. Instead, we can use Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration.
However, since the samara is falling with a constant speed, its acceleration is zero. Therefore, the net force acting on the samara is also zero.
In summary, the upward force required to keep the samara at a constant speed of 1.0 m/s is equal to the gravitational force pulling it downward, and is balanced by the force of air resistance.
To find the upward force needed to keep the fruit at a constant speed of 1.0 m/s, we can start by considering the forces acting on the samara.
Since the samara is falling at a constant speed, we know that the net force acting on it must be zero. This means that the upward force exerted on the samara must balance the downward force due to gravity.
The force due to gravity, also known as weight, can be calculated using the equation:
Weight = mass x gravity
where mass is the mass of the samara and gravity is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
In this case, the mass of the samara is given as 1.31 g, which is equivalent to 0.00131 kg. So, the weight of the samara can be calculated as:
Weight = 0.00131 kg x 9.8 m/s^2 = 0.0128 N (rounded to four decimal places)
Since the upward force must balance the weight, the upward force needed to keep the samara at a constant speed of 1.0 m/s is equal to the weight, which is approximately 0.0128 N.
Regarding kinematics, it is not necessary to use kinematics to find the upward force in this question. Kinematics deals with the motion of objects and includes concepts such as acceleration, velocity, and displacement. Since the question states that the samara is falling at a constant speed, implying no acceleration, we don't need to use kinematics to find the upward force. We can solely rely on Newton's second law (net force = mass x acceleration) and the fact that the net force must be zero in this case.