Two blocks A and B are connected to each other. The spring is massless and pulley is frictionless. Block B slides over the horizontal top surface of stationary block C and the block A slides along the vertical side of the same block C both with same uniform speed. The co-efficient of friction between the blocks is \(0.2\) and the spring has a spring constant of \(1960\frac{N}{m}\). If the mass of block A is \(2kg\). Calculate: (i) Mass of block B? and. (ii) Energy stored in spring.
Ans: \(m_{B}=10kg\) and \(U=0.098J\).
A locomotive of mass \(m\) starts moving so that its velocity varies according to the equation given; \(v=\alpha\sqrt{s}\), where \(\alpha\) is constant and \(s\) is the distance covered. Find: the total work done by all the forces acting on the locomotive during first \(tsec\) after the beginning of the motion.
Ans: \(W=\frac{1}{8}m\alpha^{2}t^{2}\).
An engine of weight \(6.4MT\) is going up an inclined plane of \(5\) in \(13\) at the rate of \(9\frac{km}{h}\). If the co-efficient of friction is \(\frac{1}{12}\). Take \(g=10\frac{m}{s^{2}}\). calculate: the power of engine.
Ans: \(P=73.4kW\).
A particle of mass \(m\) is moving in a horizontal circle of radius \(r\), under a centripetal force equal to \(\left(\frac{K}{r^{2}}\right)\). Where: K is constant. What is total energy of the particle?
Ans: \(E=-\frac{K}{2r}\).
A small object of mass \(mg\) hangs from a string of length \(1m\). A variable force which starts at \(0(Zero)\) and gradually increases is used to pull the object very slowly (so, that equilibrium exists all the times) until the string makes an angle \(\theta\) with the vertical. Calculate: the work done by the force.
Ans: \(W=mg(1-Cos\theta)\).
The kinetic energy of a particle moving along a circular track of radius \(R\) depends on the distance covered \(S\) as \(K=\alpha.S^{2}\). Where: \(\alpha\) is constant. Find: the force acting on particle as function of \(S\).
Ans: \(F=2\alpha.S\sqrt{1+\frac{S^{2}}{R^{2}}}\).
A force \(\vec{F}=-k\left(y\hat{i}+x\hat{j}\right)\) where \(k\) is positive constant, acts on a particle moving in x-y plane. Starting from the origin, the particle is taken along x-axis to a point \(\left(a,0\right)\) and then parallel to y-axis to the point \(\left(a,a\right)\). Calculate: the total work done by the force on the particle.
Ans: \(W=-ka^{2}\).
A ball whose K.E is E, is projected at an angle of \(45^{o}\) to the horizontal. What will be the kinetic energy of the ball at the highest point of its flight?
Ans: \(E’=\frac{E}{2}\).
A bullet of mass m moving with a velocity is embedded into a block of mass M suspended by a thread. As a result of this collision, the block along with the bullet rises to a height h. Prove that velocity of bullet was \(\left(\frac{m+M}{m}\right)\sqrt{2gh}\).
A body of mass m accelerates uniformly from rest to velocity \(v_{1}\) in time \(t_{1}\). What will be the instantaneous power delivered by the body as a function of time?
