Physics Answers

1. A pinball machine launch ramp consisting of a spring and a 30 degree 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.

what will be the value of acceleration due to gravity at a height of the radius of the earth , from the surface of the earth what will be the value of acceleration due to gravity at a height of the radius of the earth , from the surface of the earth

On the horizontal table, there are ten identical little cubes in a row.

The cubes are not bonded together in any way. Squeeze the entire chain with the two outermost cubes in your palms. Which force F should you use to squeeze the cubes off the table and split them apart? Each cube has a mass of m, and the coefficient of friction between cubes is.

A light rod of length L and a little weight of mass m make up the pendulum. In a vertical plane, the rod can complete a full rotation. The weight is initially in the bottom equilibrium position. A horizontally directed velocity v is applied to the weight. What values of v will cause the pendulum to oscillate, and what values will cause it to rotate in the vertical plane? At what starting velocity v will the rod be crushed at the top point, and at what initial velocity v will it be stretched?

Consider an ideal diatomic gas that performs a reversible thermodynamic cycle that consists of a succession of the following transformations.

A → B: isobar expansion from volume VA to the volume VB = 2 · VA;

B → C: isochoric transformation;

C → D: isobar expansion up to the volume VD = 3 · VA;

D → A: isothermal compression that closes the cycle.

Calculate the efficiency of this reversible cycle

Simple pendulum has its maximum speed at the ________

The pattern of a standing wave consists of 5 loops. If the length of the string is L, then the distance between two consecutive node-antinode is:

A rod 0.5 m long floats vertically in a liquid with 0.3 m above the surface. What is the density of the rod if the relative density of the liquid is 1.2?

The area of the body of a man is about 2.5 m². Find the force exerted on him by Earth's atmosphere when he is at an altitude of 50 m.

A standing wave on a 1.5 m rope has three nodes. What is the wavelength?