A 650 N student stands on a scale in an elevator. As the elevator starts to move, the scale reads 780 N.
a. Find tha acceleration.
b. Is the elevator going up or down?
a. Since Fnet = m a, a = Fnet/m
Now we need values for the net force and the mass.
Fnet = 780 - 650 = 130 kg m/s^2
is the net force acting on the student.
The mass m is weight/g = 650/g
= 66.3 kg
a = 130/66.3 = 1.96 m/s^2
b. The student could be accelerating while going up, or decelerating while going down.
a. Well, it seems like this student has been consuming a few too many donuts lately because they're gaining weight - in terms of the scale reading, that is! To find the acceleration, we'll need to consider the net force acting on the student.
The net force can be calculated by subtracting the normal force (equal to the student's weight) from the scale reading force. So, the net force is 780 N - 650 N, which gives us 130 N.
Using Newton's second law, which states that force equals mass times acceleration (F = ma), we can find the acceleration. However, we'll first need to convert the weight (650 N) into mass.
Assuming the acceleration due to gravity is approximately 9.8 m/s², we divide the weight by the acceleration due to gravity to find the mass:
650 N / 9.8 m/s² ≈ 66.33 kg
Now we can find the acceleration:
130 N = 66.33 kg * a
Solving for a:
a ≈ 1.96 m/s²
Therefore, the acceleration of the elevator is approximately 1.96 m/s².
b. Ah, the age-old question of "up or down" – a true existential crisis for elevators! But fear not, dear friend, we can determine the direction based on the readings of the scale.
Since the scale reading is greater than the student's weight, it means the net force is in the upward direction.
So, to answer your question, the elevator is going up! It's taking our student friend to new heights (and hopefully not too many more donut shops).
To solve this problem, we can use 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.
Given:
Weight of the student = 650 N
Reading on the scale = 780 N
a. Find the acceleration:
Since the scale reading is greater than the weight of the student, there must be an additional force acting on the student. This additional force is equal to the net force experienced by the student inside the elevator.
Net Force = Reading on Scale - Weight of the Student
Net Force = 780 N - 650 N
Net Force = 130 N
Using Newton's second law, we can find the acceleration:
Net Force = Mass of the Student × Acceleration
130 N = Mass of the Student × Acceleration
Now, since we don't have the mass of the student, we need to convert the weight (N) to mass (kg) by using the formula:
Weight = Mass × Gravitational Acceleration
Rearranging the formula to solve for Mass:
Mass = Weight / Gravitational Acceleration
Gravitational Acceleration is approximately 9.8 m/s².
Mass = 650 N / 9.8 m/s²
Mass = 66.33 kg (approximately)
Now, substituting the known values into the equation:
130 N = 66.33 kg × Acceleration
Solving for Acceleration:
Acceleration = 130 N / 66.33 kg
Acceleration ≈ 1.96 m/s²
b. Is the elevator going up or down:
Since the net force acting on the student is in the upward direction (130 N > 0 N), we can conclude that the elevator is moving upwards.
To answer these questions, we need to understand the concept of force. In this case, we are dealing with gravitational force and the force experienced by the student on the scale.
a. To find the acceleration, we can use 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.
The force experienced by the student on the scale is the normal force, which is equal in magnitude to the gravitational force. Therefore, the force experienced by the student is 780 N.
The weight or gravitational force can be calculated using the formula: weight = mass × gravitational acceleration.
Given that the weight is 650 N, we can rearrange the formula to find the mass: mass = weight ÷ gravitational acceleration.
The gravitational acceleration is approximately 9.8 m/s² (on Earth).
So, the mass of the student would be: mass = 650 N ÷ 9.8 m/s².
Once we have the mass, we can use Newton's second law to calculate the acceleration: acceleration = force ÷ mass.
Plugging in the values, we get: acceleration = 780 N ÷ (650 N ÷ 9.8 m/s²).
b. To determine if the elevator is going up or down, we need to compare the scale reading (780 N) to the weight of the student (650 N).
When the elevator is at rest or moving with a constant velocity (not accelerating), the scale reading will be equal to the weight of the person. In this case, the scale reading is greater than the weight of the student (780 N > 650 N).
Therefore, the scale reading indicates a larger force than just the gravitational force. This additional force indicates an upward force due to the acceleration of the elevator, meaning the elevator is moving upward.
By following these steps and calculations, we can find the acceleration of the elevator and determine its direction of movement.