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Answer :
To find the coefficient of friction between the road and the tires of the car, let's follow these steps:
1. Understand the Problem:
- A car with a weight of 8500 N is traveling at 20 m/s.
- The car skids for 200 meters before coming to a stop.
- We need to find the coefficient of friction.
2. Apply the Work-Energy Principle:
- The work done against friction is equal to the change in kinetic energy of the car.
- Initial kinetic energy (KE_initial) = 0.5 × mass × velocity².
- Since the car comes to rest, the final kinetic energy (KE_final) = 0.
3. Calculate the Mass of the Car:
- The weight of the car is also the force due to gravity, which is `mass × gravity (g)`.
- Rearrange to find mass: `mass = weight / g`.
- Here, `gravity g = 9.8 m/s²`.
- So, `mass = 8500 N / 9.8 m/s²`.
4. Find the Initial Kinetic Energy:
- KE_initial = 0.5 × mass × (20 m/s)².
5. Relate Work Done to Friction:
- Work done by friction = force of friction × distance.
- Force of friction = coefficient_of_friction × normal force.
- Normal force is the same as the weight of the car since the motion is horizontal, which is 8500 N.
6. Solve for Coefficient of Friction:
- Work done by friction = initial KE.
- `coefficient_of_friction = initial KE / (weight_of_car × distance_skid)`.
After performing these calculations, we find:
- The initial kinetic energy is approximately 173,469.39 Joules.
- The coefficient of friction is approximately 0.102.
So the coefficient of friction between the road and the tires is closest to option A) 0.1.
1. Understand the Problem:
- A car with a weight of 8500 N is traveling at 20 m/s.
- The car skids for 200 meters before coming to a stop.
- We need to find the coefficient of friction.
2. Apply the Work-Energy Principle:
- The work done against friction is equal to the change in kinetic energy of the car.
- Initial kinetic energy (KE_initial) = 0.5 × mass × velocity².
- Since the car comes to rest, the final kinetic energy (KE_final) = 0.
3. Calculate the Mass of the Car:
- The weight of the car is also the force due to gravity, which is `mass × gravity (g)`.
- Rearrange to find mass: `mass = weight / g`.
- Here, `gravity g = 9.8 m/s²`.
- So, `mass = 8500 N / 9.8 m/s²`.
4. Find the Initial Kinetic Energy:
- KE_initial = 0.5 × mass × (20 m/s)².
5. Relate Work Done to Friction:
- Work done by friction = force of friction × distance.
- Force of friction = coefficient_of_friction × normal force.
- Normal force is the same as the weight of the car since the motion is horizontal, which is 8500 N.
6. Solve for Coefficient of Friction:
- Work done by friction = initial KE.
- `coefficient_of_friction = initial KE / (weight_of_car × distance_skid)`.
After performing these calculations, we find:
- The initial kinetic energy is approximately 173,469.39 Joules.
- The coefficient of friction is approximately 0.102.
So the coefficient of friction between the road and the tires is closest to option A) 0.1.
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