3.
a traffic light is suspended by two cables. what
should be the angle between the cables (0) so that the
tension in each cable will be equal to the weight of the
traffic signal light (w=t, = t)?

120°

Explanation:

Draw a free body diagram.  There are three forces acting on the traffic light.  Two tension forces acting along the cables, and weight.

The tension forces have an angle θ between them.  That means each tension force forms an angle of θ/2 with respect to the vertical.  So the y component of each tension force is:

Ty = T cos (θ/2)

Sum of the forces in the y direction:

∑F = ma

Ty + Ty − W = 0

2 Ty = W

Substituting:

2 T cos (θ/2) = W

If W = T, then:

2 W cos (θ/2) = W

2 cos (θ/2) = 1

cos (θ/2) = 1/2

θ/2 = 60°

θ = 120°

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.