A student weighing 800N crouches on a scale and suddenly vertically upward. His roommate notices that the scale reads 900 N momentarily just as he leaves the scale. With what acceleration does he leave the scale?
100 N = (800/9.81) a
Im stuck on ...
100N= 81.549a
What do i do next?
huh?
100 = 81.55 a
so
a = 100/81.55 m/s^2
Thank you!
You are welcome.
Well, it seems like the scale had a brief moment of exaggeration when the student left! That scale couldn't make up its mind, huh? Anyway, let's crunch some numbers to figure out the acceleration.
The scale read 900 N momentarily, which means that the student experienced an extra force of 900 N. Since the student's weight is initially 800 N, we can subtract that from the 900 N to find the net force acting on the student.
Net force = 900 N - 800 N = 100 N
Now we can use Newton's second law, which states that the net force is equal to the mass of an object multiplied by its acceleration:
Net force = mass × acceleration
Since the mass of the student remains constant, we can rearrange the equation to solve for acceleration:
Acceleration = Net force / mass
Using the given net force of 100 N and assuming an average acceleration due to this upward force, we can calculate the acceleration.
Acceleration = 100 N / 80 kg (let's assume the student's mass is 80 kg)
Acceleration ≈ 1.25 m/s²
So, the student leaves the scale with an acceleration of approximately 1.25 m/s². Just remember, scales aren't always the most accurate when it comes to keeping track of your weight or your dramatic exits!
To find the acceleration with which the student leaves the scale, we need to apply Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
In this case, the net force acting on the student is the difference between his weight and the reading on the scale.
Weight = Mass × Acceleration due to gravity
Given that the weight of the student is 800 N, we can use the equation Weight = Mass × Acceleration due to gravity to determine the mass of the student.
800 N = Mass × 9.8 m/s^2 (acceleration due to gravity)
Simplifying the equation, we get:
Mass = 800 N / 9.8 m/s^2
Now, to find the acceleration with which the student leaves the scale, we'll consider the upward force acting on the student. According to Newton's third law of motion, the upward force is equal in magnitude and opposite in direction to the downward force exerted by the scale.
Therefore, the net force acting on the student is:
Net force = Upward force - Downward force
= 900 N - 800 N
= 100 N
Using Newton's second law, we can determine the acceleration:
100 N = Mass × Acceleration
Substituting the mass value we obtained earlier:
100 N = (800 N / 9.8 m/s^2 ) × Acceleration
Now, to find the acceleration, we rearrange the equation and solve for it:
Acceleration = (100 N × 9.8 m/s^2 ) / 800 N
Calculating this, we get:
Acceleration = 1.225 m/s^2
Therefore, the student leaves the scale with an acceleration of 1.225 m/s^2.