The , is a dimensionless group important in heat transfer calculations. it is defined as , where is the heat capacity of a fluid, is the fluid viscosity, and is the thermal conductivity. for a particular fluid, 0 583 j/(g c), 0 286 w/(m c), and 1936 lb /(ft h). estimate the value of without using a calculator (remember, it is dimensionless), showing your calculations; then determine it with a calculator.

What mass will a pumpkin have a force of 450 newton’s accelerates it to 110 m/s^2? include the correct units.

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 710 n/m. it is initially at rest on an inclined plane that is at an angle of θ = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. a) what is the block's initial mechanical energy? b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

The 10-kg double wheel with radius of gyration of 125mm about o is connected to the spring of stiffness k = 600 n/m by a cord which is wrapped securely around the inner hub. if the wheel is released from rest on the incline with the spring stretched 225 mm, calculate the maximum velocity v of its center o during the ensuing motion. the wheel rolls without slipping