Question

1. You've always wondered about the acceleration of the elevators in the 101 story high Empire State Building. One day, while visiting New York, you take your bathroom scale into the elevator and stand on it. The scale reads 183 lblb as the door closes. As the elevator moves upward the scale reading varies between a minimum value of 144 lblb and a maximum value of 233 lb.

a) What is your mass in kg?

b) What is the magnitude of the acceleration as the elevator starts upward?

c) What is the magnitude of the acceleration as the elevator brakes to a stop?

2. Three blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force F⃗ F→F_vec. (Figure 1) The masses of the three blocks are  MA=MA= 14.0 kg, MB= 21.8 kg, and MC= 43.1 kg, Answer the following questions concerning the motion of the blocks.

a) If the blocks move across the horizontal frictionless surface with a constant velocity of 2.5 m/s, what is the horizontal force F⃗ F→F_vec?

Answer 1

1a) Since the reading is 183 lb as the elevator door closes (elevator yet to move), hence mass = 183 lb

Or, mass = 183 * 0.453592 kg [as 1 lb = 0.453592 kg]

Or, mass = 83 kg (approx)

Thus, the mass is 83 kg.

1b) As elevator starts upward, the net force acting on person is the weight of the person plus the force of the elevator.

Or, effective force = F_e = mg + ma, where m = mass ; g = acceleration due to gravity ; a = acceleration attained

Since the mass value varied between 144 lb and 233 lb, let's take the mean of these values to calculate the effective force.

Therefore, F_e = [(144 + 233) / 2] * 0.453592 * 9.8 N

Or, F_e = 837.92 N

Thus, 837.92 = 83 * 9.8 + 83 * a = 83 (9.8 + a)

Or, a = 0.295 ms^-2

Thus, the magnitude of the acceleration is 0.295 ms^-2.

1c) As the elevator brakes to a stop, the final velocity becomes zero. Now, the reading should correspond only to the mass of the person inside it without any extra component. Thus, the acceleration is zero when the elevator brakes to a stop.

2a) Since the horizontal surface is frictionless, the co-efficient of static friction is zero. Also, since the blocks are moving with constant velocity, we understand that there is no acceleration, implying that there is the net force applied on the system along the horizontal direction is zero.

Since the weights of the blocks act vertically downwards along the center of gravity, they result in a normal force acting vertically upwards, which do not necessarily contribute to the horizontal movement of the blocks.

Thus, the horizontal force applied is zero.