1)You are working in a research group investigating more energy efficient city buses. One option is to store energy in the rotation of a flywheel when the bus stops and then use it to accelerate the bus. The flywheel under consideration is a light-weight but extremely strong disk of carbon fibre composite, with a heavy iron rim of mass 51.7 kg. The proposed radius of the disk is 1.49 m.
Your boss is concerned that the ring may end up spinning so quickly that the bearings would overheat. To see if this is likely, you've been asked to work out how rapidly (in radians per second) the wheel would be spinning if it started from rest, and absorbed all the energy of motion of a bus of mass 29707.53 kg when it decelerates from a speed of 13.31 m/s down to a halt. The answer should have at least one decimal place.
2)The automatic flag raising system on a horizontal flagpole attached to the vertical outside wall of a tall building has become stuck. The management of the building wants to send a person crawling out along the flagpole to fix the problem. You have been asked to consult with a group to decide whether or not this is possible. You are all too aware that no one could survive the 80 m fall from the flagpole to the ground. The flagpole is a 61.63 kg steel I-beam which is very strong and rigid. One side of the flagpole is attached to the wall of the building by a hinge so that it can rotate vertically. 11.2 m away, the other end of the flagpole is attached to a strong, lightweight cable. The cable goes up from the flagpole at an angle of 29.10º to the horizontal until it reaches the building where it is bolted to the wall. The mechanic who will climb out on the flagpole weighs 75.97 kg including equipment. Your boss has asked you to calculate the tension in the cable when the mechanic is at the end of the flagpole. The answer should have at least one decimal place in Newtons. g=9.8[m/s^2]
Sorry for having you read such a long text like this...
Your boss is concerned that the ring may end up spinning so quickly that the bearings would overheat. To see if this is likely, you've been asked to work out how rapidly (in radians per second) the wheel would be spinning if it started from rest, and absorbed all the energy of motion of a bus of mass 29707.53 kg when it decelerates from a speed of 13.31 m/s down to a halt. The answer should have at least one decimal place.
2)The automatic flag raising system on a horizontal flagpole attached to the vertical outside wall of a tall building has become stuck. The management of the building wants to send a person crawling out along the flagpole to fix the problem. You have been asked to consult with a group to decide whether or not this is possible. You are all too aware that no one could survive the 80 m fall from the flagpole to the ground. The flagpole is a 61.63 kg steel I-beam which is very strong and rigid. One side of the flagpole is attached to the wall of the building by a hinge so that it can rotate vertically. 11.2 m away, the other end of the flagpole is attached to a strong, lightweight cable. The cable goes up from the flagpole at an angle of 29.10º to the horizontal until it reaches the building where it is bolted to the wall. The mechanic who will climb out on the flagpole weighs 75.97 kg including equipment. Your boss has asked you to calculate the tension in the cable when the mechanic is at the end of the flagpole. The answer should have at least one decimal place in Newtons. g=9.8[m/s^2]
Sorry for having you read such a long text like this...