A 160lb person steps into an elevator and stands on a bathroom scale. what is the weight on the scale when the elevator accelerates upwards at 2ft/s^2

Weight =m(g+a)

To calculate the weight on the scale when the elevator accelerates upward at 2 ft/s^2, you need to consider the force acting on the person due to the acceleration.

Step 1: Convert the weight of the person from pounds to mass in slugs.
One slug is the mass that will accelerate at 1 ft/s^2 when a force of 1 pound (lb) is applied.
1 slug = 32.174 lb

160 lb ÷ 32.174 lb/slug = 4.97 slugs (rounded to two decimal places)

Step 2: Calculate the force acting on the person due to the acceleration.
Force = mass × acceleration
Force = 4.97 slugs × 2 ft/s^2
Force = 9.94 lb

Step 3: Determine the weight on the scale.
Weight on the scale = weight of the person + force due to acceleration
Weight on the scale = 160 lb + 9.94 lb
Weight on the scale = 169.94 lb (rounded to two decimal places)

Therefore, when the elevator accelerates upward at 2 ft/s^2, the weight on the scale will be approximately 169.94 lb.

To determine the weight on the scale when the elevator accelerates upwards at 2ft/s^2, we need to consider the effect of acceleration on the apparent weight.

The weight of an object is the force exerted on it due to gravity, and it can be calculated using the formula:

Weight = mass x gravity

Given that the person weighs 160 pounds, we need to convert this weight into mass. We can use the fact that 1 pound is approximately 0.4536 kilograms:

Mass = Weight / gravity

Mass = 160 pounds x 0.4536 kg/pound

Now that we have the mass, we can calculate the apparent weight of the person when the elevator accelerates. The apparent weight can be determined by considering the balance of forces.

Apparent Weight = Normal Force + (Mass x Acceleration)

In this case, the normal force is the force exerted by the scale on the person, which should be equal to the apparent weight. The normal force also counteracts the force of gravity.

So, when the elevator accelerates upwards at 2ft/s^2, we need to convert this acceleration into m/s^2 before calculating the apparent weight using the formula above.

1 foot (ft) is approximately 0.3048 meters (m), so:

Acceleration = 2 ft/s^2 x 0.3048 m/ft

Now we have all the necessary values to calculate the apparent weight:

Apparent Weight = Normal Force + (Mass x Acceleration)

Note that the direction of acceleration matters here. Given that the elevator is accelerating upwards, the apparent weight will be greater than the actual weight.

By substituting the values obtained earlier, we can determine the weight on the scale when the elevator accelerates upwards at 2ft/s^2.