A 0.2 kg sponge is dropped from rest , pulled down by gravity. How fast will it be traveling in 6.0s , if a 0.5 N force of air resistance acts on it
weight = .2 * 9.81 = 1.96N
drag = .5N
net downward force = 1.46N
f = ma
a = 1.46/.2 = 7.3
v = at = 7.3 * 6 = 43.8 m/s
Well, well, well... looks like our little sponge is in some trouble! Let's see what we can calculate here. We know the mass of the sponge is 0.2 kg, and we have a force of air resistance acting on it, which is 0.5 N. So, to find the speed of the sponge after 6.0 seconds, we need to use some good old physics.
Using Newton's second law (F = ma), we can find the acceleration of the sponge by dividing the force by its mass. So, the acceleration is 0.5 N divided by 0.2 kg, which gives us an acceleration of 2.5 m/s².
Now, while we have this acceleration, we can use another equation, the kinematic equation, to find the speed of the sponge after 6.0 seconds. The equation for that is V = u + at, where V is the final velocity, u is the initial velocity (which is 0 m/s since it's dropped from rest), a is the acceleration, and t is the time.
Plugging in our values, we have V = 0 + (2.5 m/s²) × (6.0 s). Doing the math, we get V = 15 m/s.
So there you have it! After 6.0 seconds, despite the pesky air resistance, our sponge will be traveling at a cool 15 meters per second. Have a splashing time!
To solve this problem, we need to consider the forces acting on the sponge. The force of gravity is pulling it downward, while the force of air resistance is opposing its motion.
First, let's calculate the acceleration of the sponge without air resistance. We can use Newton's second law of motion:
Force = mass × acceleration
Rearranging the formula for acceleration:
acceleration = Force / mass
Since the force of gravity is acting on the sponge, the equation becomes:
acceleration = (mass × gravitational acceleration) / mass
The mass of the sponge is given as 0.2 kg, and the gravitational acceleration is approximately 9.8 m/s².
acceleration = (0.2 kg × 9.8 m/s²) / 0.2 kg
acceleration = 9.8 m/s²
Now, let's calculate the velocity of the sponge after 6.0 seconds. We can use the following formula:
velocity = initial velocity + (acceleration × time)
Since the sponge is dropped from rest, the initial velocity is 0 m/s.
velocity = 0 m/s + (9.8 m/s² × 6.0 s)
velocity = 58.8 m/s
However, we need to take into account the force of air resistance. The force of air resistance can be considered proportional to the velocity of the sponge. So, we can modify the equation as follows:
velocity = F_air resistance / mass × time
We are given that the force of air resistance is 0.5 N.
velocity = (0.5 N / 0.2 kg) × 6.0 s
velocity = 1.5 m/s
Therefore, when the force of air resistance acts on the sponge, it will be traveling at a speed of approximately 1.5 m/s after 6.0 s.
To find the speed of the sponge after 6.0s, we need to consider the effects of gravity and air resistance on the sponge. Let's break down the problem into steps:
Step 1: Calculate the force of gravity
The force of gravity acting on an object can be calculated using the equation:
F_gravity = m * g
where F_gravity is the force of gravity, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the sponge is 0.2 kg, we can calculate the force of gravity:
F_gravity = 0.2 kg * 9.8 m/s^2 = 1.96 N
Step 2: Calculate the net force acting on the sponge
The net force acting on the sponge is the difference between the force of gravity and the force of air resistance. Since the air resistance is acting in the opposite direction, we subtract it from the force of gravity:
Net force = F_gravity - F_air
Given that the force of air resistance is 0.5 N, we can calculate the net force:
Net force = 1.96 N - 0.5 N = 1.46 N
Step 3: Calculate the acceleration of the sponge
Using Newton's second law of motion, we can find the acceleration of the sponge by dividing the net force by its mass:
a = Net force / m
Given that the mass of the sponge is 0.2 kg and the net force is 1.46 N, we can calculate the acceleration:
a = 1.46 N / 0.2 kg = 7.3 m/s^2
Step 4: Calculate the final velocity of the sponge
To find the final velocity of the sponge after 6.0s, we can use the equation of motion:
v = u + a * t
where v is the final velocity, u is the initial velocity (which is 0 m/s since the sponge is dropped from rest), a is the acceleration, and t is the time.
Given that the initial velocity is 0 m/s, the acceleration is 7.3 m/s^2, and the time is 6.0s, we can calculate the final velocity:
v = 0 + 7.3 m/s^2 * 6.0 s ≈ 43.8 m/s
Therefore, the sponge will be traveling at approximately 43.8 m/s after 6.0s, accounting for the 0.5 N force of air resistance acting on it.