Hwk. Problem: Work, Energy, Power

In summary, a 5000 kg runaway truck with failed brakes is moving at 146 km/h before the driver steers. It then travels up a frictionless emergency escape ramp with an inclination of 15°. The minimum length L of the ramp can be found using the equation Vf^2 - Vi^2 = 2gh, where Vf is the final speed (0 m/s) and Vi is the initial speed (40.6 m/s). The mass of the truck does not affect the minimum length, but a decrease in speed will result in a decrease in the minimum length. The minimum length can also be found by equating the initial kinetic energy to the final potential energy.
  • #1
shawonna23
146
0
A runaway truck with failed brakes is moving downgrade at 146 km/h just before the driver steers, the truck travels up a frictionless emergency escape ramp with an inclination of 15°. The truck's mass is 5000 kg.


(a) What minimum length L must the ramp have if the truck is to stop (momentarily) along it? (Assume the truck is a particle, and justufy that assumption.)


I know that the minimum length stays the same if the truck's mass is decreased. and the minimum length decreases if the truck's speed is decreased.

I am clueless on what equation to use to find the minimum length L. Can someone please help me out.
 
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  • #2
Think conservation of energy. As the truck moves up the ramp, its kinetic energy is transformed into gravitational potential energy. So... how high does the truck rise? Then use a bit of trig to find the length of the ramp.
 
  • #3
To find the height, I used the equation:

Vf^2-Vi^2 divided by 2g. Is the vfinal=40.6m/s and vinitial=0?

Am I using the right equation?
 
  • #4
You have the values of vfinal and vinitial mixed up, and you have them mixed up in the equation. Technically not correct, but the mistakes cancel out to give the correct height.
 
  • #5
The mass is not necessary here.You have two ways for the result,1) Because it stopes, the square of the initial speed must be equal with double of L*acceleration which is g or sin15. From here you can find L.2)The phenomen is in the gravitational field - conservative , so the total energy is the same (equal) at the beginning and at final.If we consider on start is the level zero so the potential energy is 0,and the body has only Kinetic=msquarev:2.It is= with the final where because stopped ,has not kinetic but has potential Wp= mgh where h is l*sin15. So if you write on a paper this eqaution you will obtain the same result like 1).
 

Related to Hwk. Problem: Work, Energy, Power

1. What is the difference between work and energy?

Work is the measure of the force applied to an object multiplied by the distance the object moves in the direction of the force. Energy, on the other hand, is the ability to do work. It is the product of force and distance, and can exist in various forms such as kinetic, potential, thermal, and chemical energy.

2. How is power related to work and energy?

Power is the rate at which work is done or energy is transferred. It is the amount of work done or energy transferred per unit of time. Mathematically, power is equal to work divided by time, or energy divided by time.

3. Can work and energy be negative?

Yes, both work and energy can be negative. This occurs when the force and movement are in opposite directions, resulting in a decrease in the object's energy. For example, when a car is braking, work is being done on the brakes and the car's kinetic energy is decreasing.

4. What is the relationship between work, energy, and force?

Work, energy, and force are all interrelated concepts. Work is the result of a force acting on an object, and energy is the ability of an object to do work. Therefore, work and energy are both dependent on force. The greater the force applied to an object, the more work is done and the more energy is transferred.

5. How can the conservation of mechanical energy be applied to solve problems?

The conservation of mechanical energy states that the total energy of a system remains constant, as long as there is no external work or non-conservative forces acting on the system. This principle can be applied to solve problems involving work, energy, and power by equating the initial and final energy values and setting them equal to each other. This allows for the unknown variables to be solved for.

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