Mechanics | Relativity Answers

How much power is needed to lift a 4.5 kg object to a height of 3.0 m in 12 s?

An object moving at 15 m/s has a kinetic energy of 8500 J. What must be the speed of the same object that has kinetic energy of 6300 J.

Three identical balls with masses of M, 2M, and 3M are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is ?

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A string is wrapped around a solid disk of radius R that sits on a frictionless incline with angle theta as shown. The string is pulled up the plane with Tension T in such a way that it unwinds without slipping from the disk and the disk rolls without slipping down the incline. What is the linear acceleration (a) of the the disk down the plane.

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 Without the wheels, a bicycle frame has a mass of 7.77 kg. Each of the wheels can be roughly modeled as a uniform solid disk with a mass of 0.820 kg and a radius of 0.343 m. Find the kinetic energy of the whole bicycle when it is moving forward at 4.05 m/s

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.)

2. 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?

According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy "Dizzy"Carlyle in a minor league game. The ball traveled 196.4 meters before landing on the ground outside the ballpark. Assuming the ball's initial velocity was in a direction 45° above the horizontal and ignoring air resistance, what did the initial speed of the ball,in meters per second, need to be to produce such a home run if the ball was hit at a point 0.7 m above the ground level? How far would the ball be above a fence 3.0 meters high if the fence was 98 meters from the home plate? Write your answer in meters.

The rear wheel of a 150 kg tricycle accidentally ran over a nail. The circular tip of the nail has a diameter of 0.001 m. How much pressure did the wheel of the tricycle experience assuming that the entire weight of the tricycle is concentrated on the rear wheel that ran over the nail.

Given two vectors A=6i + 3j - k and B = 4i -5j + 8k , find the magnitude of the vector 2A - 3B.