A student stands on a scale in an elevator that is accelerating at -2 m/s2. If the student has a mass of 97 kg, to the nearest newton what is the scale reading?
Well, it seems like this student has got quite the elevator ride going! To determine the scale reading, we need to consider the forces acting on the student. We have the force due to gravity pulling the student downward, which is equal to the mass multiplied by the acceleration due to gravity (approximately 9.8 m/s^2). So, the force due to gravity is approximately 97 kg × 9.8 m/s^2 = 950.6 N.
Since the elevator is accelerating downward, there's an additional downward force opposing the force due to gravity. By Newton's second law (F = ma), the force is equal to the mass multiplied by the acceleration. So, the additional downward force is approximately 97 kg × (-2 m/s^2) = -194 N.
To determine the scale reading, we simply add these forces together: 950.6 N + (-194 N) ≈ 756.6 N. So, the nearest newton reading on the scale would be around 757 N.
Now, let's just hope this student isn't too "down" about their weight measurements in this accelerated elevator.
To find the scale reading, we need to consider the forces acting on the student. Firstly, there is the force of gravity acting downwards, which can be calculated using the formula:
Force of gravity = mass x acceleration due to gravity
Given that the mass of the student is 97 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force of gravity:
Force of gravity = 97 kg x 9.8 m/s^2 = 950.6 N
Since the elevator is accelerating downward at -2 m/s^2, there is an additional force acting on the student. This force can be calculated using Newton's second law:
Force = mass x acceleration
The mass of the student is still 97 kg, and the acceleration is -2 m/s^2:
Force = 97 kg x (-2 m/s^2) = -194 N
To find the scale reading, we need to add these forces together since they act in the same direction (downward):
Scale reading = Force of gravity + Force from acceleration
= 950.6 N + (-194 N)
= 756.6 N
Therefore, to the nearest newton, the scale reading is approximately 757 N.
To find the scale reading, we need to consider the forces acting on the student. In this case, there are two forces: the force of gravity and the normal force from the scale.
First, let's calculate the force of gravity acting on the student. The force of gravity can be calculated using the formula:
force of gravity = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2 (usually rounded to 10 m/s^2 for simplicity).
force of gravity = 97 kg * 10 m/s^2
force of gravity = 970 N
So, the force of gravity acting on the student is 970 Newtons.
Next, let's consider the normal force from the scale. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the scale provides the normal force.
Since the elevator is accelerating downwards at -2 m/s^2, it means there is a net force acting on the student that is greater than the force of gravity. Therefore, the normal force from the scale must be greater than the force of gravity to provide the additional force necessary for the student to accelerate downwards.
To calculate the normal force, we need to consider the net force acting on the student. The net force is given by the equation:
net force = mass * acceleration
net force = 97 kg * (-2 m/s^2)
net force = -194 N
Since the net force is negative, we can deduce that the normal force is more than 194 N to compensate for the acceleration downwards.
Now let's calculate the scale reading, which is equal to the normal force exerted by the scale on the student.
Scale reading = normal force
Since the normal force is greater than 194 N and the force of gravity acting on the student is 970 N, we can approximate the scale reading to the nearest newton by adding the force of gravity to the normal force:
Scale reading = 970 N + 194 N
Scale reading = 1164 N
Therefore, to the nearest newton, the scale reading is 1164 N.