Need help with question 2 please. 1. A 200kg roller-coaster car is on a friction

Question

Need help with question 2 please.

1. A 200kg roller-coaster car is on a frictionless track initially moving at 3 m/s at the top of the first hil. What is the speed of the roller coaster at each of the peaks of the rest of the hills (a,b) and when it reaches ground level (c)? 20m 5m 2. If the roller-coaster track was not frictionless and when the coaster reached point c it had a speed of 10 m/s, how much work must have been done by the frictional force? 3. An object is sliding along a flat surface with an initial speed of 30 m/s. What must the coefficient of kinetic friction be between the object and the surface if the object slides to a stop in 10m? What would be the speed of the object after it had only slide half that distance? 4. A 10 kg box is dropped from a height of 50m. Just before it hits the ground it is clocked to have a speed of 30m/s! Was energy conserved in this situation? If not, how much work was done by non-conservative forces? 5. Is it possible to do negative work on an object that is initially at rest? 6. Let's look at the "impact" of work/KE! Consider an old car from the 60's that was built a little more rigid. You could fall asleep behind the wheel, crash into a tree, wake up and be like what!? Then put it in reverse and drive home assuming you are not too badly shaken up! A new car would be totaled if you hit a tree like that with any significant speed. So why?! Let's assume we have two cars that have the same mass (2000kg). These cars are driving straight at a tree with a speed of 30 m/s (67 mph). The first car is built rigid as to not destroy the car during impact and after the collision has some bumper damage but the damage is only as thick as the bumper. Let's call it about 15cm. The second car is build less rigid and crumples most of the length of the front of the car This car crumples a length of approximately 60cm. Using work/KE, what is the force exerted on each car (and thus directly influencing your day!) if we assume the force is constant? Discuss the results in terms of car construction

Explanation / Answer

2. Work done by friction = total initial energy - energy at ponit c

This will give positive magnitude, however work done by friction is negative as displacement is done in opposite direction of frictional force

Total initial energy = mgh = 200 x 9.81 x 20 = 39240 J

Total energy at point c = 1/2 mv2 = 0.5 x 200 x 102 = 10000 J

Hence, work done by friction = -29240 J (decrease in energy is due to friction)

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