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. I didn't understand the answer when I plugged in the numbers.
f = m (g+a)
f= 700n/9.81 kg (9.81 + 1.8)
I get 828440.367
i move the decimal point over 3 places to the left and get 828 kN
The answer the book gives is .83 k N
What am I doing wrong ? help
You are missing quite a lot on metric system.
700N/9.81m/s^2= 71 kg
71kg(9.8m/s^2+1.8m/s^2)=828N=.83kN
282.908318
To solve this problem, you are on the right track by using the formula f = m(g + a), where f is the force measured by the scale, m is the mass of the person, g is the acceleration due to gravity, and a is the acceleration of the elevator.
However, there are a few mistakes in your calculation. Let's break it down step by step:
1. Mass (m) calculation:
Since the force (f) is given in Newtons (N), and the formula requires mass in kilograms (kg), you need to convert the force to kg using the equation f = m × g, where g is the acceleration due to gravity (approximately 9.81 m/s^2). In this case, the force f is 700 N, so:
700 N = m × 9.81 m/s^2
m = 700 N / 9.81 m/s^2 ≈ 71.3 kg
Therefore, the mass of the person is approximately 71.3 kg.
2. Calculation of the total force:
Now that you have the correct mass, you can use the formula f = m(g + a) to find the force recorded by the scale. In this case, g = 9.81 m/s^2 and a = 1.8 m/s^2 (upward acceleration):
f = 71.3 kg × (9.81 m/s^2 + 1.8 m/s^2)
f ≈ 71.3 kg × 11.61 m/s^2
f ≈ 827.6 N
Therefore, the scale reading should be approximately 827.6 N.
Make sure to double-check your math calculations, particularly with units and significant figures, as it seems you made errors with decimal placement. The book's answer of 0.83 kN (830 N) is quite close to your calculated answer of 827.6 N, so it's possible you made a rounding error.
Remember that 1 kN (kilonewton) is equal to 1000 N (newtons). Thus, you can convert the answer to kN by dividing it by 1000:
827.6 N / 1000 = 0.8276 kN (rounded to four decimal places)
Therefore, the correct scale reading, rounded to two decimal places as given in the book, is approximately 0.83 kN.