The 2000 kg cable car descends a 200-m-high hill. In addition to its brakes, the

Question

The 2000 kg cable car descends a 200-m-high hill. In addition to its brakes, the cable car controls its speed by pulling an 1800 kg counterweight up the other side of the hill. The rolling friction of both the cable care and the counterweight are negligible.

A. How much braking force does the cable car need to descend at a constant speed?

B. One day the brakes fail just as the cable care leaves the top on it's downward journey.  What is the runaway car's speed at the bottom of the hill.

NOTE: It is important that you please be really specific when explaining how you solve the problem.  We are expecting to be able to explain each step in solving - Please help.

Explanation / Answer

There are only 2 forces acting on the counterweight. They are Sin20*mg and the force of tension on the cable. Because the mass of the cable car is greater, it's pulling the counterweight over and down the hill.

First I found (I think) the force of the breaks.

Total forces on cable car = Ft+Fb-sin30*m*g

Total forces on counterweight = Ft-sin20*m*g

To find the the force on the breaks I set equation 2 as: Tension = sin20*m*g and I get approx. 6335 N. Then I inserted it into the equation for the cable car and set acceleration = 0 since the problem mentioned constant speed.

I then subtract that from the force of gravity on the cable car (sin30*m*g = 10094 N) and get Force of breaks = 3759 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.