Physics Answers

A standing wave on a string of length L = 3 m fixed at both ends is described by: y(x,t) = 0.01sin⁡(πx)cos⁡(40t), where x and y are in meters and t is in seconds. The maximum transverse speed of an element on the string located at x = 1/6 m is:

3. A target in a shooting board consists of a vertical square wooden board, 0.250 m on a side and with a mass 750 g and pivots around a horizontal axis along its top edge. The board is stuck faceon at its center by a bullet of mass 1.90 g, travelling at 360 m/s that remains embedded in the board.

(a) (2 marks) What is the angular speed of the board just after the bullet’s impact?

(b) (2 marks) What maximum height does the center of the board reach from the equilibrium before it starts swinging down again?

(c) (2 marks) What minimum bullet speed is needed for the board to swing all the way over after the impact?

A solid sphere of mass 2 kg and a massless string of total length 4 meters which is wrapped around the equator of the sphere (total length includes the length of wrapped string and the length of the string hanging from the ceiling). The sphere then falls vertically while rolling down (without slipping) the whole wrapped string and falls on top of an inclined plane. Due to the collision with the inclined plane, it loses all its kinetic energy within a very short time and starts rolling along the inclined plane with zero initial velocity. Consider that a total of 10 Joules of energy is lost during the motion of the sphere along the planes.The magnitude of gravitational acceleration g = 9.8 𝑚/𝑠2. (a) Find the value of the moment of inertia of the sphere about its axis of rotation.(b) What is the magnitude of angular velocity of the sphere when it touches the inclined plane?(c) How far along the second inclined plane (45º) on the right will the center of the sphere travel before it comes to a stop?

A pinball machine launch ramp consisting of a spring and a 30∘ ramp of length L.

(a) (3 marks) If the spring is compressed a distance 𝑥 from its equilibrium position and is then released at 𝑡 = 0, the pinball (a sphere of mass 𝑚 and radius 𝑟) reaches the top of the ramp at 𝑡 = 𝑇. Derive the expression for the spring constant 𝑘 in terms of 𝑚, 𝑔, 𝑥, and 𝐿.[Assume that the friction is sufficient, and the ball begins rolling without slipping immediately after launch.]

(b) (2 marks) What is the potential energy of the ball when it is at the midpoint of the ramp?

(c) (3 marks) Derive the expression of the speed of the ball immediately after being launched in terms of 𝑔 and 𝐿. 

How do I deduce the width of a refractive glass block

An electric circuit is formed of :

_a generator delivering a constant voltage Ugenerator=24 volt

_Resistor D of resistance R=48 ohm

_Rheostat (D') of adjustable resistance R_h

1_Show applying law of addition of voltages that the current is given by the expression:

I=U_generator/R+R_h

2_We vary the value of R_h between two limiting values 0 ohm and 120 ohm.Calculate the value I₁ of I for R_h=0 ohm.Then calculate the value I₂ of I for R_h=120 ohm.

3_Deduce the role of a rheostat in a series connection.

4_Let P be the power dissipated by R.Give the expression of P in terms of R and I.Calculate the value P₁ of P for I=I₁ and the value of P₂ of P for I=I₂

5_The maximum power that the resistor D can stand is 5 watt. Show that resistor D can be damaged only in one of the two limiting values of R_h.

A pinball machine launch ramp consisting of a spring and a 30∘ ramp of length 𝐿 as shown in Fig. 1.

(a) (3 marks) If the spring is compressed a distance 𝑥 from its equilibrium position and is then released at 𝑡 = 0, the pinball (a sphere of mass 𝑚 and radius 𝑟) reaches the top of the ramp at 𝑡 = 𝑇. Derive the expression for the spring constant 𝑘 in terms of 𝑚, 𝑔, 𝑥, and 𝐿. [Assume that the friction is sufficient, and the ball begins rolling without slipping immediately after launch.]

(b) (2 marks) What is the potential energy of the ball when it is at the midpoint of the ramp?

(c) (3 marks) Derive the expression of the speed of the ball immediately after being launched in terms of 𝑔 and 𝐿

A large number of neon atoms are in thermal equilibrium. What is the ratio of the number of atoms in a 5s state to number in 3p state at (a) 300K; (b) 600K; (c) 1200K? The energy difference between two states is 1.96 eV. (d) at any of these temperatures, the rate at which a neon gas spontaneously emits 632.8nm radiation is quite low. Explain why? 

A car acceleration of 1m/s². What is the change in its velocity after every 3 seconds?

A Carnot refrigerator rejects 2500 kJ of heat at 80°C while using 1100 kJ of work