6. Intro to Forces (Dynamics)

A 50 kg box hangs from a rope. What is the tension in the rope if: The box has v_y = 5.0 m/s and is speeding up at 5.0 m/s²

A 50 kg box hangs from a rope. What is the tension in the rope if: The box moves up at a steady 5.0 m/s?

Astronauts in space 'weigh' themselves by oscillating on a spring. Suppose the position of an oscillating 75 kg astronaut is given by $x=\left(0.30\text{m}\right)\sin \left(\right(\pi \text{rad/s})\times t)$, where t is in s. What force does the spring exert on the astronaut at (a) t = 1.0 s and (b) 1.5 s? Note that the angle of the sine function is in radians.

The mass of the sun is 2.0 x 10³⁰ kg. A 5.0 x 10¹⁴ kg comet is 75 million kilometers from the sun. What is the magnitude of the comet's acceleration toward the sun?

A woman has a mass of 55 kg. What is her weight while standing on earth?

It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10 m/s. A 60 kg passenger gets aboard on the ground floor. What is the passenger's weight after the elevator reaches its cruising speed?

It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10 m/s. A 60 kg passenger gets aboard on the ground floor. What is the passenger's weight before the elevator starts moving?

Zach, whose mass is 80 kg, is in an elevator descending at 10 m/s. The elevator takes 3.0 s to brake to a stop at the first floor. What is Zach's weight before the elevator starts braking?

FIGURE EX6.19 shows the velocity graph of a 75 kg passenger in an elevator. What is the passenger's weight at t=1s? At 5 s? At 9 s?

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

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.

What will a spring scale read for the weight of a 58.0‑kg woman in an elevator that moves 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 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 with a downward acceleration 0.18 g?

(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.