6. Intro to Forces (Dynamics)

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) A narrow but solid spool of thread has radius R and mass M. If you pull up on the thread so that the cm of the spool remains suspended in the air at the same place as it unwinds, what force must you exert on the thread?

(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?

A 6750-kg helicopter accelerates upward at 0.80m/s² while lifting a 1080-kg frame at a construction site, Fig. 4–66. What is the tension in the cable (ignore its mass) which connects the frame to the helicopter?

A 6750-kg helicopter accelerates upward at 0.80m/s² while lifting a 1080-kg frame at a construction site, Fig. 4–66.

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(c) What force does the cable exert on the helicopter?

A wet bar of soap (m = 150g) slides freely down a ramp 3.0 m long inclined at 8.5°. How long does it take to reach the bottom? How would this change if the soap's mass were 250 g?

A 265-kg load is lifted 18.0 m vertically with an acceleration a = 0.140 g by a single cable. Determine the tension in the cable.