Please show every step of the solutions. Many thanks in advance! As a simple pen

Question

Please show every step of the solutions. Many thanks in advance!

As a simple pendulum swings back and forth, the forces acting on it are gravity, the tension in the supporting cord and air resistance, (a) Which of these forces, if any, does no work on the pendulum? (b) Which of these forces, if any, does negative work at all times during the motion, (c) Describe the work done by the gravitational force while the pendulum is swinging. Can kinetic energy be negative? Explain. Let A = 5.0 m at 60degree above the horizontal axis. Let B have a magnitude of 10 m. If = 43.3 m2 find the angle theta AB between the vectors and all possible solutions for B A force F = N acts on a particle that undergoes a displacement Find (a) The work done by the force on the particle and (b) the angle between F and A force N acts on an object as the object moves in the x direction from the origin to x = 5 m. Find the work done by the force on the object.

Explanation / Answer

1) a) W = F d cos theta

since T has angle 90 degrees, W = 0

all rest do work

so Tension does no work

b) air resistance does negative work

c) gravity does postive work when going down and negative when going up

2) since KE = 1/2 mv^2
m >0 and v^2>0

KE is always positive

3) A*B = A B cos theta

cos theta = 43.3/(5*10)

theta = arcos(43.3/(5*10))= 30 degrees

so either at 90 degrees or 30 degrees, with 10 m magnitude

4)

a) W =F*r = 6*3 -2*1 = 18 - 2 = 16 J

b) F*dr = F dr cos theta

cos theta = 16/(sqrt(6^2+2^2)*sqrt(3^2+1^2)

theta = 36.87 degrees

5)
so dr = dx ihat
W = integral of F dr = integral 4 x dx = 2 x^2 from 0 to 5 = 2*25 = 50 J

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