Two identical steel cubes (masses 50g, side 1cm) collide head-on face to face with a speed of 10cm/s each. Find the maximum compression of each. Young’s modulus for steel = Y= 2 × 10¹¹ N/m².

Two identical steel cubes (masses 50g, side 1cm) collide head-on face to face with a speed of 10cm/s each. Find the maximum compression of each. Young’s modulus for steel = Y= 2 × 10¹¹ N/m².

An engine is attached to a wagon through a shock absorber of length 1.5m. The system with a total mass of 50,000 kg is moving with a speed of 36 km h^-1 when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, calculate the spring constant.

Two springs A and B (k_A = 2k_B) are stretched by applying forces of equal magnitudes at the four ends. If the energy stored in A is E. that in B is

Consider the situation of the previous problem. Suppose the block of mass m₁ is pulled by a constant force F₁, and the other block is pulled by a constant force F₂. Find the maximum elongation that the spring will suffer.

Consider one mole of perfect gas in a cylinder of unit cross section with a piston attached (Fig. 12.12). A spring (spring constant k) is attached (unstretched length L) to the piston and to the bottom of the cylinder. Initially the spring is unstretched and the gas is in equilibrium. A certain amount of heat Q is supplied to the gas causing an increase of volume from V_o to V₁.

(a) What is the initial pressure of the system?

(b) What is the final pressure of the system?

(c) Using the first law of thermodynamics, write down a relation between Q, P_a, V, V_o and k.

Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is

Two blocks of masses m₁ and m₂ are connected by a spring of spring constant k (figure 9-E15). The block of mass m₂ is given a sharp impulse so that it acquires a velocity u₀ towards right. Find (a) the velocity of the center of mass, (b) the maximum elongation that the spring will suffer.

Two masses m₁ and m₂ are connected
by a spring of spring constant k and are placed on a frictionless horizontal surface. Initially the spring is stretched through a distance x0 when the system is released from rest. Find the distance moved by the two masses before they again come to rest.