Related InterviewSolutions

• Calculate the kinetic energy of a tractor crawler belt of mass `m` if the tractor moves with a velocity `v`. There is no slipping. Neglect the size of the wheels.
• A uniform cylinder of radius `r` and mass `m` can rotate freely about a fixed horizontal axis. A thin cord of length l and mass `m_(0)` is would on the cylinder in a single layer. Find the angular acceleration of the cylinder as a function of the length `x` of the hanging part of the end. the wound part of the cord is supposed to have its centre of gravity on the cylinder axis is shown in figure.
• A smooth light horizontal rod AB can rotate about a vertical axis passing through its end A. The rod is fitted with a small slieeve of mass m attached to the end A by a weightless spring of length `l_0` and stiffness `x`. What work must be performed to slowly get this system going and reaching the angular velocity `omega`?
• Two relativistic particles move at right angles to each other in a laboratory frame of reference, one with the velocity `v_1` and the other with the velocity `v_2`. Find their relative velocity.
• A point traversed half the distance with a velocity `v_0`. The remaining part of the distance was covered with velocity `v_1` for half the time, and with velocity `v_2` for the other half of the time. Find the mean velocity of the point averaged over the whole time of motion.
• The kinetic energy of a particle moving along a circle of radius R depends on the distance covered s as `T=as^2`, where a is ticle as a function of s.
• A locomotive of mass m starts moving so that its velocity varies according to the law `V=alphasqrts,` where `alpha` is a constant and s is the distance covered. Find the total work done by all the forces acting on the locomotive during the first t seconds after the beginning of motion.
• A solid body starts rotating about a stationary axis with an angular acceleration `alpha=(2.0xx10^(-2))trad//s^(2)` here `t` is in seconds. How soon after the beginning of rotation will the total acceleration vector of an arbitrary point of the body form an angle `theta=60^(@)` with its velocity vector?
• At the moment `t=0` a stationary particle of mass m experiences a time-dependent force `F=at(tau-t)`, whera a is a constant vector, `tau` is the time during which the given force acts. Find: (a) the momentum of the particle when the action of the force discontinued: (b) the distance covered by the particle while the force acted.
• A cannon and a target are `5.10 km` apart and located at the same level. How soon will the shell launched with the initial velocity `240 m//s` reach the target in the absence of air drag?