a 700 N man stands on a scale on the floor of an elevator. The scare records the force it exerts on whatever is on it. What is the scale reading if the elevator has an acceleration of 1.8 m/s squared up ? I need help with what formula (s) to use to get the answer. Thanks in advance.
To accelerate up, the sale needs to exert an upward force equal to his weight (m g) PLUS m a, where a is the acceleration.
Thus the measured weight it
F = m (g + a)
Now, since m = (700 N)/g
F = 700 N + 700 N (a/g)
= 700 [1 + (a/g)] N
In your case, a = 1.8 and g = 9.8, both in m/s^2
To determine the scale reading, we need to consider the forces acting on the man inside the elevator.
The formula we can use to solve this problem is Newton's second law:
F_net = m * a
In this case, the net force acting on the man is the sum of his weight (mg) and the force exerted by the scale.
To calculate the net force, first we need to determine the weight (mg) of the man. The weight of an object is given by the formula:
Weight = mass * acceleration due to gravity
Since the problem doesn't provide us with the mass of the man, we can use the formula:
Weight = mass * acceleration due to gravity
Given that the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the mass of the man using the formula:
Weight = mass * acceleration due to gravity
Rearranging the formula to solve for mass:
mass = Weight / acceleration due to gravity
After calculating the mass of the man, we can use it to find the net force by using Newton's second law:
F_net = m * a
In this case, the net force is the force exerted by the man and the scale. The acceleration (a) is given as 1.8 m/s^2.
Finally, the scale reading is equal to the force exerted by the man on the scale, which is the net force:
Scale reading = F_net
Plug in the values and calculate to find the scale reading.
To find the scale reading, we need to consider the forces acting on the man in the elevator.
The forces acting on the man are his weight (W = mg) and the normal force (N) exerted by the scale. When the elevator is accelerating upward, the net force on the man is the difference between these two forces.
Let's break it down step-by-step:
Step 1: Determine the weight of the man
Given that the man's weight is 700 N, we can use the formula:
W = mg
where m is the mass of the man and g is the acceleration due to gravity (approximately 9.8 m/s²).
Therefore, we can calculate:
700 N = m × 9.8 m/s²
Step 2: Calculate the mass of the man
Rearrange the formula from Step 1 to solve for m:
m = W / g
Substitute the given values:
m = 700 N / 9.8 m/s²
Step 3: Determine the net force on the man
When the elevator moves upward with an acceleration of 1.8 m/s², the net force on the man is the difference between the weight (force due to gravity) and the normal force exerted by the scale. This can be calculated using Newton's second law:
Net Force = ma
where m is the mass of the man and a is the acceleration.
Therefore:
Net Force = m × a
Step 4: Calculate the net force on the man
Substitute the values we calculated in Steps 2 and 3 into the equation:
Net Force = (700 N / 9.8 m/s²) × 1.8 m/s²
Step 5: Determine the scale reading
The scale reading is equal to the normal force exerted by the scale on the man.
According to Newton's third law, the normal force exerted by the scale is equal in magnitude and opposite in direction to the force the man exerts on the scale.
Therefore, the scale reading is equal to the net force on the man (opposite in direction):
Scale Reading = -Net Force
Step 6: Calculate the scale reading
Substitute the value of the net force from Step 4 into the equation:
Scale Reading = -((700 N / 9.8 m/s²) × 1.8 m/s²)
After performing the calculations, you should have the scale reading on the elevator scale. Remember, the negative sign indicates that the scale reading will be in the opposite direction to the acceleration of the elevator.