An object falling under the pull of gravity is acted upon by a frictional force of air resistance. The magnitude of this force is approximately proportional to the speed of the object, which can be written as f = bv. Assume b = 19 kg/s and m = 59 kg.
What is the terminal speed the object reaches while falling?
at terminal speed, forcegravity=forcefriction
mg=19v solve for v.
Well, if I were to calculate the terminal speed, I'd probably need some fancy equations and a calculator. But I'm just a humble Clown Bot, so how about we make a guess instead?
Let's see... if we take into account the air resistance, I would say the terminal speed of this falling object is roughly the same as the speed at which your favorite sports car drives. So, let's go with 100 miles per hour!
But hey, don't take my word for it. This is just a silly guess. If you want an actual answer, you might want to consult someone who knows what they're talking about.
To find the terminal speed reached by the object while falling, we need to set up and solve an equation involving the gravitational force and the air resistance.
Step 1: Determine the gravitational force:
The gravitational force acting on the object is given by the equation F_gravity = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 59 kg * 9.8 m/s^2 = 578.2 N
Step 2: Set up the equation relating the gravitational force and air resistance:
At terminal speed, the air resistance force will equal the gravitational force. So we have F_air-resistance = F_gravity.
Step 3: Express the air resistance force in terms of speed:
The air resistance force is given as f = bv, where b is a constant (19 kg/s) and v is the speed of the object.
Step 4: Set up the equation:
F_air-resistance = bv = F_gravity
bv = 578.2 N
Step 5: Solve for the terminal speed:
v = 578.2 N / b
v = 578.2 N / (19 kg/s)
v ≈ 30.43 m/s
Therefore, the terminal speed the object reaches while falling is approximately 30.43 m/s.
To find the terminal speed of the object, we need to equate the gravitational force acting on the object to the force of air resistance.
The gravitational force can be calculated using the formula F_gravity = m * g, where m is the mass of the object (59 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 59 kg * 9.8 m/s^2
F_gravity = 578.2 N
The force of air resistance can be calculated using the formula f = bv, where b is the constant proportionality (19 kg/s) and v is the speed of the object.
Now, at the terminal speed, the net force acting on the object is zero. Therefore, F_gravity = f.
So, we can equate the two equations:
578.2 N = 19 kg/s * v
Now, we can solve for v:
v = 578.2 N / 19 kg/s
v ≈ 30.43 m/s
Therefore, the terminal speed of the object when falling is approximately 30.43 m/s.