Calculating Work to Stop a 1000 kg Car at 100 km/hr

  • Thread starter rueberry
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In summary, to stop a 1000 kg car traveling at 100 km/hr, the amount of work required is approximately 386,000 Joules. This can be calculated using the formula KE=1/2mv^2, assuming no friction. To convert from km/hr to m/s, the conversion factor is 1000/3600 = 0.277. However, the book uses a more accurate ratio of 100*1000/3600, resulting in a slightly different answer of 386,000 Joules.
  • #1
rueberry
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How much work is required to stop a 1000 kg car traveling at 100 km/hr?

I was going to use KE=1/2mv^2 , since the work should equal the KE, assuming no friction.

I have: =1/2(1000 kg)(100km/hr)^2

I was using dimensional analysis to make the conversion to m/s, so I end up with J, but I think I'm doing something wrong in the conversion.

(1000 km/hr)(1000 m/1 km)(3600 sec/1 hr)
 
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  • #2
rueberry said:
How much work is required to stop a 1000 kg car traveling at 100 km/hr?

I was going to use KE=1/2mv^2 , since the work should equal the KE, assuming no friction.

I have: =1/2(1000 kg)(100km/hr)^2

I was using dimensional analysis to make the conversion to m/s, so I end up with J, but I think I'm doing something wrong in the conversion.

(1000 km/hr)(1000 m/1 km)(3600 sec/1 hr)
To get Joules, the conversion factor from km/hr to m/s is: 1000/3600 = .277. 1 km/hr = .277 m/sec; 100 km/hr = 27.7 m/sec.

AM
 
  • #3
When I work that problem out, I get 383645J, but the answer in the book says 386,000J. Am I doing something wrong? If I use 27.7 m/sec in the equation, I get

1/2(1000kg)(27.7m/sec)=383645
 
  • #4
The book is using the ratio 100*1000/3600 [=27 7/9] and not the approximation 27.7 m/s.
 

1. How is work calculated?

Work is calculated by multiplying the force applied to an object by the distance over which the force is applied. In mathematical terms, work = force x distance.

2. What is the equation for calculating work?

The equation for calculating work is W = F x d, where W is work, F is force, and d is distance.

3. How do you calculate the force needed to stop a 1000 kg car at 100 km/hr?

To calculate the force needed to stop a 1000 kg car at 100 km/hr, you can use the equation F = m x a, where F is force, m is mass, and a is acceleration. First, convert 100 km/hr to m/s by dividing by 3.6. Then, use the mass of the car (1000 kg) and the final velocity of 0 m/s to calculate the acceleration. Finally, plug in the values to solve for force.

4. What is the distance required to stop a 1000 kg car at 100 km/hr?

The distance required to stop a 1000 kg car at 100 km/hr depends on the force applied and the friction between the car's tires and the road. Using the equation W = F x d, you can rearrange it to solve for distance (d = W / F). If you know the force required to stop the car and the work done, you can calculate the distance needed to stop the car.

5. How can you apply this concept in real life?

Calculating work to stop a 1000 kg car at 100 km/hr is a real-life application of the laws of physics. This concept is used in car safety design and braking systems, as well as in understanding the forces involved in car accidents. It also demonstrates the importance of considering mass, velocity, and friction when applying a force to an object.

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