A loading car is at rest on a track forming an angle of 25◦ with the vertical when a force is applied to the cable attached at C. The gross weight of the car and its load is 5500 lb, and it acts at point G. Knowing the tension in the cable connected at C is 5000 lb, determine (a) the acceleration of the car, (b) the distance the car moves in 20 s, (c) the time it takes for the car to return to its original position if the cable breaks after 20 s.

The motion of the car along the inclined plane reduces the force required

to pull the car upwards.

The correct values are

(a) The acceleration of the car upwards is approximately 0.09 ft./s².

(b) The distance the car moves in 20 s. is approximately 18 ft.

(c) The time it takes the car to return to its original position is approximately 1. seconds.

Reasons:

(a) Component of the car's weight acting along the incline plane, = W·sin(θ)

∴ = 5500 lbf × cos(25°) ≈ 4984.69 lbf.

The force pulling the car upwards, F = T -

Which gives;

F = 5,000 lbf - 4984.69lbf = 15.31 lbf

The mass of the car, m ≈ 170.95 lbf

The acceleration of the car, a ≈ 0.09 ft./s².

(b) The distance the car moves is given by the kinematic equation of

motion, s = u·t + 0.5·a·t², derived from Newton Laws of motion.

Where;

u = The initial velocity of the car = 0 (the car is initially at rest)

t = The time taken = 20 seconds

a = The acceleration ≈ 0.09 ft./s²

∴ s ≈ 0 × 20 + 0.5 × 0.09 × 20² = 18

The distance the car moves, s ≈ 18 ft.

(c)  If the cable breaks, we have;

Force acting downwards on the car = Weight of the car acting on the plane

∴ Force acting downwards on the car = = 4984.69 lbf

Therefore;

Which gives;

The time it takes car to travel the 18 ft. back to its original position is given as follows;

s = u·t + 0.5·a·t²

The initial velocity, u= 0

Therefore;

Which gives;

The time it takes the car to return to its original position, t ≈ 1. seconds

Learn more here:

link

Check attachment for solution

Explanation:

from 1609, galileo galilei used the recently invented telescope to observe the sun, moon and planets. he saw the mountains and craters of the moon, and for the first time revealed the planets to be worlds in their own right. galileo also provided strong observational evidence that planets orbited the sun.

his discoveries about the moon, jupiter's moons, venus, and sunspots supported the idea that the sun - not the earth - was the center of the universe, as was commonly believed at the time.galileo turned his gaze toward venus, the brightest celestial object in the sky - other than the sun and the moon.

wavelegth as in spectrum red oygbiv