You know your mass is 69 kg , but when you stand on a bathroom scale in an elevator, it says your mass is 78 kg. What is the magnitude of the acceleration of the elevator?
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To calculate the magnitude of the acceleration of the elevator, we can use Newton's second law of motion. The equation is given by:
F_net = m * a
Where F_net is the net force, m is the mass, and a is the acceleration.
In this case, the net force acting on you is your weight, which is equal to the product of your mass and the acceleration due to gravity (9.8 m/s^2).
So, the equation becomes:
F_net = m * g
The net force is also equal to your apparent weight, which is the difference between your true weight and the normal force exerted by the scale.
In this case, your apparent weight is 78 kg * g, and your true weight is 69 kg * g.
Therefore,
78 kg * g = 69 kg * g + N
Simplifying the equation, we get:
9 kg * g = N
To determine the magnitude of the acceleration of the elevator, we can use the equation N = m * a, where m is the mass and a is the acceleration.
Substituting the values, we have:
9 kg * g = 69 kg * a
Dividing both sides by 69 kg, we get:
a = (9 kg * g) / 69 kg
Calculating the value, we find:
a ≈ 1.30 m/s^2
Therefore, the magnitude of the acceleration of the elevator is approximately 1.30 m/s^2.
To determine the magnitude of the acceleration of the elevator, we can use Newton's second law of motion:
F = m * a
Where:
F is the force acting on the object,
m is the mass of the object,
a is the acceleration.
In this scenario, your mass is 69 kg, and the scale is reading a mass of 78 kg. It is important to note that the reading on the scale represents the force being exerted on the scale, not the mass.
Since the scale is measuring the force, we need to convert the scale reading to force using the acceleration due to gravity. The force exerted on an object is given by:
Force = mass * acceleration due to gravity
In this case, the force is equal to the mass recorded by the scale (78 kg) multiplied by the acceleration due to gravity (9.8 m/s²). So we have:
Force = 78 kg * 9.8 m/s² = 764.4 N
Now, we can equate this force to the force calculated by Newton's second law:
764.4 N = 69 kg * a
Solving for acceleration (a), we obtain:
a = 764.4 N / 69 kg = 11.09 m/s²
Therefore, the magnitude of the acceleration of the elevator is approximately 11.09 m/s².
Scale*g=mg+ma solve
scale= m(1+a/g)
78=69(1+a/g)
solve for a.