Mechanics | Relativity Answers

Prove collision (of tennis ball) was elastic with a Velocity - time graph (Tip: calculate the distance)

Consider a rod of mass 4m and length 2r

connected to two spheres A and B of identical

masses m. Balls of mass m fall right above

sphere A at certain rate that causes the rod

system to rotate such that, when sphere B

reaches the position of A it gets hit by a falling

ball with velocity v.

1 Calculate the angular velocity of the system ωn+1 after it gets hit by ball

number n in terms of ωn, v and r.

2 The rotating system reaches ultimately a constant rotational velocity ω0.

Express ω0 as function of c and r.

3 How reaching a constant ω0 is still consistent with conservation of energy.

4 What would be the ultimate rotational velocity ω0 if the rotating system

includes two roads making a cross shape, and each end is connected to a

sphere of mass m.

When the level of mercury in the attached branch of manometer that 

means the gas pressure in the reservoir is

Two waves travelling in the same direction are given by: y1 = 0.2 sin⁡(2πx-20t+φ) and y2 = 0.2 sin⁡(2πx-20t), where x and y are in meters and t is in seconds. If the two waves start at the same moment, then the path difference, ∆x, corresponding to a fully destructive interference is:

2/3 m

3/4 m

1/3 m

1/2 m

4/3 m

Two transverse sinusoidal waves combining in a string are described by the wave functions y1 = 0.02 sin⁡(2πx+πt) and y2 = 0.02 sin(2πx-πt), where x and y are in meters, and t is in seconds. If after superposition, a standing wave of 3 loops is formed, then the length of the string is:

2 m

1.5 m

0.75 m

0.5 m

1 m

Two waves travelling in the same direction are given by: y1 = 0.2 sin⁡(3πx-20t+φ) and y2 = 0.2 sin⁡(3πx-20t), where x and y are in meters and t is in seconds. If the two waves start at the same moment, then the path difference, ∆x, corresponding to a fully destructive interference is:

1/2 m

1/3 m

3/4 m

2/3 m

4/3 m

 standing wave on a stretched string with a tension force F_T and of length L = 2 m has the following equation: y(x,t) = 0.1 sin⁡(2πx) cos⁡(100πt). How many loops would appear on the string if the velocity is increased by a factor of 2 while the frequency is held constant?

4 loops

12 loops

8 loops

2 loops

6 loops

Clear selection

The equation of a standing wave is y(x,t) = 0.8 cos⁡(0.1πx) sin⁡(200πt) where x and y are in cm and t is in seconds. The separation distance between two consecutive nodes is:

40 cm

20 cm

5 cm

2.5 cm

10 cm

Clear selection

Two identical waves travel in the same direction, each with a wavelength λ = 1 m and speed v = 20 m/s. When the two waves interfere, they form a resultant wave. The angular frequency of the resultant wave is:

40π rad/s

π/10 rad/s

π/5 rad/s

20π rad/s

80π rad/s

The left end of a taut string of length L, is connected to a vibrator with a fixed frequency f. The right end of the string is tied to a suspended object of varying mass, m, through a pulley. For a mass m1 of the object, a standing wave with one loop is observed. For a mass m2 of the object, a standing wave with two loops is observed. What is the ratio "m2 / m1 = ?"

0.0625

0.25

2

4

16