As part of a physics experiment, you stand on a bathroom scale in an elevator. Though your normal weight is 690 N, the scale at the moment reads 588 N.
(a) Is the acceleration of the elevator upward, downward, or zero?
(b) Calculate the magnitude of the elevator's acceleration.
m/s2
(c) What, if anything, can you say about the velocity of the elevator?
Explain.
please I need help. Thanks
Weight is the force with which the object presses the stationary support. Weight may be less or greater than the force of gravity (mg) in dependence on the downward or upward motion, => Weight = N, but directed in the opposite direction
vector (ma)= vector (mg)+vector( N)
for upward motion: -ma=mg-N
N=ma+mg
for downward motion: ma=mg-N
N= mg –ma - this is the given case
mg=690 N, N=588N, m=mg/g=690/9.8=70.4 kg
588 =690 - ma
a=( 690-588)/70.4= 1.45 m/s²
You don't have to give me the answer but explaining a way to get there would help
(a) Well, if the scale is reading a lower value than your normal weight, it means the scale is measuring a smaller force acting upon you. So, the elevator's acceleration must be downward.
(b) To calculate the magnitude of the elevator's acceleration, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the difference between your normal weight (690 N) and the scale reading (588 N):
Net force = 690 N - 588 N = 102 N
Now, we need to determine the mass of the object (you). Using Newton's second law, we can rearrange the equation to solve for acceleration:
Acceleration = Net force / Mass
Assuming a mass of 70 kg (just for illustrative purposes), we can calculate:
Acceleration = 102 N / 70 kg ≈ 1.46 m/s²
So, the magnitude of the elevator's acceleration is approximately 1.46 m/s².
(c) Based on the information given, we cannot determine the velocity of the elevator. The scale reading only tells us the net force acting on you, but it does not provide any insight into the velocity. Velocity is a measure of the speed and direction of motion, and the scale reading alone does not give us any information about its value or direction.
To answer these questions, we need to analyze the situation using Newton's laws of motion.
(a) To determine the direction of the elevator's acceleration, we need to compare the normal weight with the reading on the scale.
The normal weight is 690 N, but the scale reading is 588 N. Since the scale reading is less than the normal weight, it means the apparent weight is reduced, and this happens when the elevator is accelerating downward. This implies that the acceleration of the elevator is downward.
(b) To calculate the magnitude of the elevator's acceleration, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a).
In this case, the force is equal to the normal weight (690 N) minus the scale reading (588 N). So the force is 102 N (690 N - 588 N).
Using Newton's second law, we can rearrange the equation to solve for acceleration: a = F/m.
Since we know the force (102 N) and the mass is typically not provided, we can't calculate the exact acceleration without it.
(c) Regarding the velocity of the elevator, we cannot determine its exact value based solely on the information provided. However, we can say that if the elevator is accelerating downward (as determined in part a), then the velocity of the elevator is likely decreasing or becoming more negative. This is because acceleration and velocity have opposite signs when an object is slowing down or changing direction.