Ch 06: Dynamics I: Motion Along a Line
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Problem 6
A horizontal rope is tied to a 50 kg box on frictionless ice. What is the tension in the rope if: (b) The box moves at a steady 5.0 m/s?Problem 6
A 20,000 kg rocket has a rocket motor that generates 3.0 x 10^5 N of thrust. Assume no air resistance. (a) What is the rocket's initial upward acceleration?Problem 6
Compressed air is used to fire a 50 g ball vertically upward from a 1.0-m-tall tube. The air exerts an upward force of 2.0 N on the ball as long as it is in the tube. How high does the ball go above the top of the tube? Neglect air resistance.Problem 6
An accident victim with a broken leg is being placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of 4.0 kg, and the doctor has decided to hang a 6.0 kg mass from the rope. The boot is held suspended by the ropes, as shown in FIGURE P6.40, and does not touch the bed. a. Determine the amount of tension in the rope by using Newton's laws to analyze the hanging mass. Hint: If the pulleys are frictionless, which we will assume, the tension in the rope is constant from one end to the other.
Problem 6
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?
Problem 6
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. (a) What is Zach's weight before the elevator starts braking?Problem 6
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 (a) Before the elevator starts moving?Problem 6
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 (c) After the elevator reaches its cruising speed?Problem 6
A woman has a mass of 55 kg. (a) What is her weight while standing on earth?Problem 6
The mass of the sun is 2.0 x 10^30 kg. A 5.0 x 10^14 kg comet is 75 million kilometers from the sun. What is the magnitude of the comet's acceleration toward the sun?Problem 6
Astronauts in space 'weigh' themselves by oscillating on a spring. Suppose the position of an oscillating 75 kg astronaut is given by x = (0.30 m) sin ((đťť… rad/s) X 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.Problem 6
A ball is shot from a compressed-air gun at twice its terminal speed. a. What is the ball's initial acceleration, as a multiple of g, if it is shot straight up?Problem 6
(a) Above what speed does a 3.0-mm-diameter ball bearing in 20°C water experience quadratic drag?Problem 6
(b) Below what speed does a 3.0-mm-diameter ball bearing in 20°C air experience linear drag?Problem 6
So-called volcanic 'ash' is actually finely pulverized rock blown high into the atmosphere. A typical ash particle is a 50-micrometer-diameter piece of silica with a density of 2400 kg/m^3. (a) How long would it take this ash particle to fall from a height of 5.0 km in vacuum?Problem 6
A 50 kg box hangs from a rope. What is the tension in the rope if: (b) The box moves up at a steady 5.0 m/s?Problem 6
A 50 kg box hangs from a rope. What is the tension in the rope if: (c) The box has vy = 5.0 m/s and is speeding up at 5.0 m/s^2Problem 6
A medium-sized jet has a 3.8-m-diameter fuselage and a loaded mass of 85,000 kg. The drag on an airplane is primarily due to the cylindrical fuselage, and aerodynamic shaping gives it a drag coefficient of 0.37. How much thrust must the jet's engines provide to cruise at 230 m/s at an altitude where the air density is 1.0 kg/m^3Problem 6
a. A spherical particle of mass m is shot horizontally with initial speed vâ‚€ into a viscous fluid. Use Stokes' law to find an expression for vâ‚“ (t), the horizontal velocity as a function of time. Vertical motion due to gravity can be ignored.Problem 6
b. A 4.0-cm-diameter, 55 g ball is shot horizontally into a tank of 40°C honey. How long will it take for the horizontal speed to decrease to 10% of its initial value?Problem 6
A 1.0-cm-diameter, 2.0 g marble is shot horizontally into a tank of 20°C olive oil at 10 cm/s. How far in cm will it travel before stopping?Problem 6
An object with cross section A is shot horizontally across frictionless ice. Its initial velocity is v₀ₓ at tâ‚€ = 0 s. Air resistance is not negligible. a. Show that the velocity at time t is given by the expression vâ‚“ = v₀ₓ --------------- 1 + Cđť“pAv₀ₓt / 2mProblem 6
An E. coli bacterium can be modeled as a sphere that has the density of water. Rotating flagella propel a bacterium through 40°C water with a force of 65 fN, where 1 fN = 1femtonewton = 10^-15 N. What is the bacterium's speed in micrometers/s?Problem 6
What is the magnitude of the acceleration of a skydiver at the instant she is falling at one-half her terminal speed?Problem 6
So-called volcanic 'ash' is actually finely pulverized rock blown high into the atmosphere. A typical ash particle is a 50-micrometer-diameter piece of silica with a density of 2400 kg/m^3. (b) How long in hours does it take this ash particle to fall from a height of 5.0 km in still air? Use the properties of 20°C air at sea level.Problem 6
In an electricity experiment, a 1.0 g plastic ball is suspended on a 60-cm-long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force F(electric) on it, causing the ball to swing out to a 20 degree angle and remain there. (a) What is the magnitude of F(electric)?
Problem 6
The forces in FIGURE EX6.9 act on a 2.0 kg object. What are the values of ax and ay, the x- and y-components of the object's acceleration?
Problem 6
A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is 1000 N, the players have equal pulls, and the angle between the two ropes is 20 degrees. How hard must each player pull to drag the coach at a steady 2.0\m/s?
Problem 6
FIGURE EX6.10 shows the force acting on a 2.0 kg object as it moves along the x-axis. The object is at rest at the origin at t = 0s. What are its acceleration and velocity at t = 6 s?
Problem 6
a. A rocket of mass m is launched straight up with thrust Fₜₕᵣᵤₛₜ. Find an expression for the rocket's speed at height h if air resistance is neglected.
