because there is 4x the amount of kinetic energy, that means when the car stops 4x as much work must be done to bring it's energy down to 0. Work depends on the force applied and the distance the object travels as that force is applied. The force applied is not any different (friction from skidding tires is the same in both cases), so the distance must increase to account for the larger required energy. 4x the energy that must be changed requires 4x the work, which requires 4x the distance. So instead of 15 m (for 30 km/hr speed) it is 60 m for 60 km/hr.
1
Work is defined as the transfer of energy between objects. Work causes the energy of an object to change. Because the energy of the ball changed by 30 J moving it from the ground to the top of the platform, this means there must have been 30 J worth of work done
30 J. Gravitational potential energy depends on the height of the object (in addition to the mass of the object and the effect of gravity ­ 9.81 m/s2 on Earth). The height of the object is the same at the top of the platform, the top of the ramp, and the top of the steps. This means that the ball will have the same amount of PEG in all locations.
The ball will only have 20 J of PEG on the second step. It tells you that the steps are evenly spaced, so that means the second step is 2/3 of the way from bottom to top. This means that it will have 2/3 the amount of energy as it does at the top. PEG is directly related to height, so if height decreases to 2/3 of its top value (the top of the step) than PEG will also decrease to 2/3 of its top value.
30 J. It tells you in the problem that there is no air resistance acting on the ball as it falls. This means that gravity is the only force acting on that ball and gravity is a conservative force. It only changes PEG into KE. if the object starts with 30 J of PEG it will end up with 30 J of KE just before it reaches the ground.
2
No. Because there is no friction on the ramp, gravity changes the PEG into KE on the down trip. If the box starts with 30 J of PEG, it will have 30 J of KE when it reaches the height just about the ground. If it has exactly the same amount of KE in both cases and the mass does not change, it will have the same of speed.
3
Block A...duh!!!
They will reach the ground with exactly the same speed ­ if the ramp is frictionless. Without friction, gravity turns PEG into KE. Regardless of the path it takes, the PEG at the bottom of the ramp is equal to 0. This means that the KE will have to be equal to the amount of PEG that the box started with. IF KE is the same in both cases and the mass of the box does not change, the speed will be the same.
If there is friction, the speed at the bottom of ramp A will be larger because it is shorter. Friction will have more chance to reduce the amount of KE in the block (do negative work). if more negative work is done, There will be less KE at the bottom. Less KE means less speed.
4