A 60.0 kg person rides in elevator while standing on a scale. The elevator has an acceleration 2.00 m/s^2 upward. What is the reading on the scale?
m=60.0
a=2.00
FN-mg=ma
FN=ma + mg
FN=m(a+g)
FN=60(2.00+9.8)
Answer 708N
It's correct
To find the reading on the scale, we need to consider the forces acting on the person in the elevator.
First, let's determine the force of gravity acting on the person. The force of gravity is given by the equation:
F_gravity = mass × gravitational acceleration,
where mass is the mass of the person and gravitational acceleration is approximately 9.8 m/s^2.
F_gravity = 60.0 kg × 9.8 m/s^2 = 588.0 N.
Next, let's consider the force of the person's weight on the scale. This force is equal to the person's mass times acceleration:
F_weight = mass × acceleration,
where acceleration is the acceleration of the elevator.
F_weight = 60.0 kg × 2.00 m/s^2 = 120.0 N.
Finally, the reading on the scale is the sum of the forces acting on the person:
Reading on scale = F_gravity + F_weight = 588.0 N + 120.0 N = 708.0 N.
Therefore, the reading on the scale is 708.0 Newtons.
If you need the scale reading in kg just divide the force by g
Well, it looks like someone's taking a trip up in the elevator! Let's crunch some numbers, shall we?
To find the reading on the scale, we need to consider the forces acting on our 60.0 kg person. We have the gravitational force pulling them downward and the normal force from the scale pushing them upward.
The acceleration of the elevator doesn't affect the gravitational force, so that remains unchanged at 9.8 m/s^2.
Now, since the elevator is accelerating upwards at 2.00 m/s^2, the normal force from the scale will be greater than the gravitational force. This is because the person needs to experience an additional force to match the upward acceleration.
To find the reading on the scale, we can use Newton's second law: Fnet = ma, where Fnet is the net force, m is the mass, and a is the acceleration.
The net force is the difference between the normal force and the gravitational force:
Fnet = normal force - gravitational force
We can express the gravitational force as mg, where g is the acceleration due to gravity:
Fnet = normal force - mg
Now let's plug in the values:
Fnet = ma
Fnet = (60.0 kg)(2.00 m/s^2)
Fnet = 120.0 N
Since the scale is pushing upward, the reading on the scale will be the magnitude of the normal force. So the reading on the scale will be 120.0 N.
Keep in mind that this is just a measurement of the force, not your weight. So don't be too hard on yourself if the number is a bit higher than you expected!