mass of passenger is 90 kg and mass of scale is 40 kg what is scale reading inside an elevator moving at 7.8 m/s2 upward? does the mass of the scale affect the scale reading ?
To find the scale reading, we need to consider the forces acting on the scale. In this case, we have the force due to gravity acting on both the passenger and the scale, and the normal force exerted by the scale.
1. Find the force due to gravity acting on the passenger:
The force due to gravity can be calculated using the equation: F = m * g
where:
- m is the mass of the passenger (90 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
So, the force due to gravity acting on the passenger is F_passenger = 90 kg * 9.8 m/s^2.
2. Find the force due to gravity acting on the scale:
Similarly, we can calculate the force due to gravity acting on the scale, considering its mass of 40 kg. So, the force due to gravity acting on the scale is F_scale = 40 kg * 9.8 m/s^2.
3. Determine the net force acting on the scale:
The net force on the scale is the difference between the force due to gravity acting on the passenger and the force due to gravity acting on the scale. Since the elevator is moving upward with an acceleration of 7.8 m/s^2, we can determine the net force using the equation: F_net = F_passenger - F_scale - m_scale * a
where:
- F_passenger is the force due to gravity acting on the passenger
- F_scale is the force due to gravity acting on the scale
- m_scale is the mass of the scale (40 kg)
- a is the acceleration of the elevator (7.8 m/s^2)
4. Calculate the scale reading:
The scale reading is equal to the magnitude of the net force experienced by the scale. So, the scale reading is equal to the absolute value of the net force: scale reading = |F_net|.
Does the mass of the scale affect the scale reading?
Yes, the scale reading is affected by the mass of the scale. As seen in step 3, the force due to gravity acting on the scale (F_scale) is subtracted from the force due to gravity acting on the passenger (F_passenger) to determine the net force. So, a greater mass of the scale would result in a larger force due to gravity, which, in turn, affects the scale reading.