Mechanics | Relativity Answers

A body of mass 3kg and volume 4 * 0.0004 m is hung from a balance graduated in Newton’s what is the reading balance when the body is

A bottle dropped from a balloon reaches the ground in 20.0 s. Determine the height of the balloon if a) it was at rest in the air and b) it was ascending with a speed of 50.0 m/s when the bottle was dropped

b) Show that there is a time dilation for a clock that moves at a relativistic velocity v relative to an

observer who is on the ground taking readings.

A Ferris wheel of radius 12m is turning about a horizontal axis through its center, such that the linear speed of a passenger on the rim is constant and equal to 9m/s.

a) What are the magnitude and direction of the acceleration of the passenger as he passes

through the lowest point in his circular motion?

A model of a helicopter rotor has four blades, each 3.40 m

long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min (a) What is the linear speed of the blade tip, in (b) What is the radial acceleration of the blade tip expressed as a multiple of the acceleration of gravity, g?

A batter hits a baseball so that it leaves the bat with an initial speed 37.0 an initial angle 53.1o, at a location. Find

a) the position of the ball at t = 2.00 s.

b) the magnitude and direction of its velocity,

when t = 2.00 s.

c) the time when the ball reaches the highest point of its flight. d) its maximum height, h.

e) its horizontal range, 𝑅.

You are operating a remote-controlled model car on a vacant tennis court. Your position is the origin of coordinates, and the surface of the court lies in the 𝑥𝑦-plane. The car, which we represent as a point, has x- and y- coordinates that vary with time according to

 a) Find the car’s coordinates and its distance from you at time t = 2.0 s.

b) Find the car’s displacement and average velocity vectors during the interval from

t = 0 s to t = 2.0 s.

c) Find the components of the average acceleration in the interval from t = 0 s to t =

2.0 s.

In a 300-m race, runner A starts from rests and accelerates at 1.6m/s2 for the first 30 m and then runs at a constant speed. Runner B starts from rests and accelerates at 2.0m/s2 for the first 30m and then runs at a constant speed. Runner A begins running as soon as the race begins but B firsts takes a nap to rest up. What is the longest nap that B can take and still not to lose the race?

1.   One morning, while little Lenlen’s mother was busy in the kitchen, Little Lenlen rolls off the bed that is 0.50 m above the floor. If the floor is hardwood, little Lenlen’s head is brought to rest in approx. 2.0 mm. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the acceleration in both cases, to determine the risk of injury. Assume that little Lenlen remains horizontal during the fall to the floor. (Note: A more complicated fall could result in a head velocity greater or less than the speed you calculate. Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s² lasting for any length of time will not cause injury, whereas an acceleration greater than 1000m/s² lasting for at least 1 ms will cause injury.)

1.     A summersault swimmer stands on a high platform jumps vertically upward with a velocity of magnitude 2.5 m/s. Air resistance maybe ignored.

a.)   At what time after moving from the platform does the swimmer have a velocity of 0.25 m/s upward?

b.)   At what time does she has a velocity of 0.25 m/s downward?

c.)   When is the displacement of the swimmer from its initial position zero?

d.)   When is the velocity of the swimmer zero?

e.)   What are the magnitude and direction of the acceleration while the swimmer is

i.)                Moving upward?  

ii.)              Moving downward?