A 10.0-kg object experiences a drag force due to air resistance. The magnitude of this drag
force depends on its speed, and obeys the equation Fdrag =(12.0 N-s/m)v + (4.00 N-s2/m2)v2.
(a) What is the terminal speed of this object if it is falling due to gravity?
(b) At what velocity (magnitude and direction) is the net force on the object half its weight?
(c) At what velocity (magnitude and direction) is the net force on the object twice its weight?
set Fdrag=mg, then solve for v.
b,c similar
To answer these questions, we will use the concept of net force and equilibrium. Let's go step by step.
(a) To find the terminal speed, we need to find the speed at which the drag force equals the gravitational force acting on the object.
The gravitational force acting on the object can be calculated using the formula:
F_gravity = m * g
where m is the mass of the object (10.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, the drag force equation is given as:
F_drag = (12.0 N-s/m) * v + (4.00 N-s^2/m^2) * v^2
At terminal speed, the drag force equals the gravitational force. So we can set up the equation:
(12.0) * v + (4.00) * v^2 = m * g
Substituting the values and solving for v, we can find the terminal speed.
(b) To determine the velocity at which the net force on the object is half its weight, we need to equate the net force to half the weight of the object.
The net force acting on the object can be calculated using the formula:
Net force = F_drag - F_gravity
We know that the net force is half the weight, so we can set up the equation:
0.5 * (m * g) = F_drag - (m * g)
Solve this equation for v to find the velocity. Don't forget to consider the direction of the velocity.
(c) Similar to part (b), to find the velocity at which the net force on the object is twice its weight, we again set up an equation.
2 * (m * g) = F_drag - (m * g)
Solve this equation for v to find the velocity. Consider the direction of the velocity.
By following these steps, you should be able to find the answers to parts (a), (b), and (c) of the question.