The 100 kg box shown above is being pulled along the x-rays bya student. The box
ID: 1674886 • Letter: T
Question
The 100 kg box shown above is being pulled along the x-rays bya student. The box slides across a rough surface, and its positionx varies with time t according to the equation x=t3+5t,where x is in meters and t is in seconds. a) determine the speed ofthe box at time t=0. b) Determine the following as functions oftime t. Indicate the units of every coefficient in your finalexpression for every quantity found. I. The kinetic energy of thebox. II. the net force acting on the box III. the power being delivered to the box c) Calculate the net work done on the box in the internal t=0to t=2s. The 100 kg box shown above is being pulled along the x-rays bya student. The box slides across a rough surface, and its positionx varies with time t according to the equation x=t3+5t,where x is in meters and t is in seconds. a) determine the speed ofthe box at time t=0. b) Determine the following as functions oftime t. Indicate the units of every coefficient in your finalexpression for every quantity found. I. The kinetic energy of thebox. II. the net force acting on the box III. the power being delivered to the box c) Calculate the net work done on the box in the internal t=0to t=2s.Explanation / Answer
You have the formula for position which is x=t^3+5t velocity is the derivative of position or dx/dt so deriving x with respect to t give you dx/dt=3t^2+5 At t=0 your velocity V(0)=dx(0)/dt=3(0)^2 + 5 V(0) = 5 For II the formula for force is F=ma acceleration is the derivative of velocity or dv/dt V=3t^2 +5 dV/dt = 6t a=6t M=100kg F=ma and F = (100 kg)*6t = 600t kg*m/s^2 Power is equal to work * distance - P=W/t Work is equal to force * distance - W=F*x So we get P=(F*x)/t F = 600t x = t^3+5t t = t P = (600t)(t^3+5t)/t = (600t^4+3000t^2)/t = 600t^3 + 3000t Watts orJoules/Second for part c just use the same definition of work W = 600t*(t^3+5t) at time t=0 no work has been done W(0)=0 at time t=2 work has been done where W(2)=600(2)*(2^3+5*2) = 21600Joules
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