If Force = (-4, 1) and Displacement = (-2,-3), find the angle in degrees between

Question

If Force = (-4, 1) and Displacement = (-2,-3), find the angle in degrees between the two vectors. A) 88 B) -52 C) 125 D) 45 E) 71 If Force = 3 x^3 - 2 x, find the work done by the force for a distance of x = 1 to x = 3. A) 0 B) 52 C) 81 D) 20 E) 60.75 A spring of spring constant of 10000 N/m and compressed by.3 m accelerates a 5 kg mass down a frictionless incline from a height of 4 m. What is the speed of the mass at the bottom of the inclined plane? A) 24 m/s B) 16 m/s C) 8.85 m/s D) 12 m/s E) 3 m/s A 500 N tightrope walker stands at the center of the rope such that each half of the rope makes an angle of 10 degree with the horizontal. What is the tension in the rope? A) 2900 N B) 1440 N C) 1000 N D) 50 N E) 500 N

Explanation / Answer

part 1 )

costheta = (-4*-2) + (1*-3) / sqrt(4^2+1^2)*sqrt(2^2+3^2)

theta = 71 degree

part 2 )

w = intergal F.dx from 1 to 3

w = 3x^4/4 - x^2 from 1 to 3

w = [ 3 * (3)^4/4 - 3^2] - [ 3/4 - 1]

w = 52 J

part c )

PE = KE

1/2*kx^2 + mgh = 1/2mv^2

v = 16 m/s

part 4 )

2Tsin10 = 500

2T use here because 2 segment of rope

T = 500/2sin10

T = 1440 N

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