6. Intro to Forces (Dynamics)

The Mars Rover Perseverance weighed about 10,000 N while on Earth. After it reached the surface of Mars, it weighed about 3790 N. What is the gravitational acceleration on Mars?

A 3-kg bucket is being pulled upwards by a cord. The tension in the cord is 35 N. What is the acceleration of the bucket? (The mass of the cord is negligible, which means you can assume m_cord = 0.)

A fisherman yanks a fish vertically out of the water with an acceleration of 2.5 m/s² using very light fishing line that has a breaking strength of 183 N (≈ 4lb) . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

(II) A rocket with a mass of 2.45 x 10⁶ kg is launched by exerting a vertical force of 3.55 x 10⁷ N on the gases it expels. Determine

(a) the acceleration of the rocket, Assume g remains constant, and ignore the mass of gas expelled (not realistic).

(II) A woman stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of her regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.

(II) What will a spring scale read for the weight of a 58.0‑kg woman in an elevator that moves

(a) upward with constant speed 4.4 m/s,

(II) What will a spring scale read for the weight of a 58.0‑kg woman in an elevator that moves

(b) downward with constant speed 4.4 m/s,

(II) What will a spring scale read for the weight of a 58.0‑kg woman in an elevator that moves

(d) with a downward acceleration 0.18 g, and

(II) An exceptional standing jump would raise a person 0.80 m off the ground. To do this, what force must a 68-kg person exert against the ground? Assume the person crouches a distance of 0.20 m prior to jumping, and thus the upward force has this distance to act over before he leaves the ground.

(II) What will a spring scale read for the weight of a 58.0‑kg woman in an elevator that moves

(e) in free fall?

(II) An 18.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 215 N and breaks as the elevator accelerates. What was the elevator's minimum acceleration (magnitude and direction)?

(III) 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.) <IMAGE>

"(II) 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. 

(a.) Determine the elapsed time for each of these 3 stages."

(III) 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

(d) 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,

(a) 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 v→ =v₀ → 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:

(a) v₀→ is downward

(II) 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?

<IMAGE>

(III) 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

(c) falls freely, and

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

(b) 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.

<IMAGE>

(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?

(II) A 265-kg load is lifted 18.0 m vertically with an acceleration a = 0.140 g by a single cable. Determine

(a) the tension in the cable;