An inclined plane, fixed to the inside of an elevator, makes a 38° angle with the floor. A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator accelerates downward at 0.50 g?

Determine a formula for the acceleration of the system shown in Fig. 4–49 (see Problem 55) if the cord has a non-negligible mass m_C. Specify in terms of ℓ_A and ℓ_B , the lengths of cord from the respective masses to the pulley. (The total cord length is ℓ_A + ℓ_B.)

High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s², and (2) the typical maximum speed attainable is about 9.0 m/s. You board an elevator on a skyscraper's ground floor and are transported 180 m above the ground level in three steps: acceleration of magnitude 1.2m/s² from rest to 9.0 m/s, followed by constant upward velocity of 9.0 m/s, then deceleration of magnitude 1.2m/s² from 9.0 m/s to rest. Determine the elapsed time for each of these 3 stages.

An inclined plane, fixed to the inside of an elevator, makes a 38° angle with the floor. A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator moves upward at constant speed?

(II) How much tension must a cable withstand if it is used to accelerate a 1400-kg car vertically upward at 0.70m/s²?

(III) An object moving vertically has $\(\overrightarrow{\mathbf{v}\)}_{}=\(\overrightarrow{\mathbf{v}\)}_0$ at t = 0. Determine a formula for its velocity as a function of time assuming a resistive force F = -bv as well as gravity for two cases: $\(\overrightarrow{\mathbf{v}\)}_0$ is downward.

As shown in Fig. 4–48, five balls (masses 2.00, 2.05, 2.10, 2.15, 2.20 kg) hang from a crossbar. Each mass is supported by '5-lb test' fishing line which will break when its tension force exceeds 22.2 N (5.00lb). When this device is placed in an elevator, which accelerates upward, only the lines attached to the 2.05 and 2.00 kg masses do not break. Within what range is the elevator's acceleration?

An inclined plane, fixed to the inside of an elevator, makes a 38° angle with the floor. A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator falls freely?