A block of 1 kg mass is pulled from rest in the horizontal x-direction with a displacement dependent force of F=4x+2. The rope makes a 30 degree angle with the floor. What is the change in kinetic energy?
2007-04-10 16:54:37 · 2 answers · asked by AdrianG430 1 in Science & Mathematics ➔ Physics
I have great respect for Cat, but I believe this question is fine:
The work is the integral of the force over the distance. Since the force is displacement dependent, yet the angle of the rope is constant then integrate the force over the range 0 to x
Cat: the integral of x dx = x^2/2
work=(2*x^2+2*x)*cos(30)
This work is equal to the change in kinetic energy.
j
2007-04-18 16:39:58 · answer #1 · answered by odu83 7 · 0⤊ 0⤋
The problem description is incomplete.
1st: if the force is F=4x+2, I assume it is directed in the x direction. But then you say "the rope makes a 30 degree angle"... does that mean that F=4x+2 is the equation of the tension in the rope?
2nd. How far is the block moved? The change in kinetic energy will be equal to the work done on the block
W = F.d = (4x+2)*x = 4x^2 + 2x
but without knowing x, you won't get a numerical value.
Oh and if F is the tension in the cord, multiply the result by cos(30)
2007-04-16 10:13:58 · answer #2 · answered by catarthur 6 · 0⤊ 0⤋