W = _|....F*dx*cos(a)........With F=force, x=distance over which force acts on object,
.......0.............................and a=angle between force and direction of travel.
Since the force is constant in this case we don't need the equation to be an integral expression, and since the force in question - the force of friction - is always precisely opposite the direction of travel (which makes (a) equal to 180 deg, and cos(a) equal to -1) the equation can be rewritted like so:
W = F*x*(-1) ............ or ............. W = -F*x
The force of friction is given by the equation: Ffriction = Fnormal*(coeff of friction)
Also, note that the total work is the sum of all 45 passes by the sandpaper. So our final equation, when Ffriction is substituted, is:
W = (-45)(Fnormal)(coeff of friction)(distance)
W = (-45)...(1.8N).........(0.92).........(0.15m)
W = ................-11.178 Joules
Answer:
2.1 rad/s
Explanation:
Given that,
Mass of a tether ball, m = 0.546 kg
Length of a rope, l = 4.56 m
The maximum tension the rope can withstand before breaking is 11.0 N
We need to find the maximum angular speed of the ball. Let v is the linear velocity. The maximum tension is balanced by the centripetal force acting on it. It can be given by :
Let 
is the angular speed of the ball. The relation between the angular speed and angular velocity is given by :
So, the maximum angular speed of the ball is 2.1 rad/s.
