A 3,000kg car rests on rough horizontal ground. A rope is attached to the car and is pulled with a force of 11,000N to the left. As a result, the car accelerates at 3 m/s^2. The coefficient of sliding friction between the car and the ground is ___. (round to the nearest hundredth)
To find the coefficient of sliding friction between the car and the ground, we can use Newton's second law of motion and the equation for friction.
1. Identify the forces acting on the car:
- The force pulling the car to the left, which we'll call the applied force (F_applied).
- The force of friction acting on the car, opposing its motion.
- The weight of the car, which acts vertically downward.
2. Write down the equation for the net force acting on the car:
Net force = F_applied - Friction force
3. Determine the weight of the car:
The weight can be calculated using the formula: weight = mass * acceleration due to gravity.
Given the mass of the car is 3,000 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we have:
Weight = 3,000 kg * 9.8 m/s^2.
4. Calculate the net force:
Since the car is accelerating to the left, the net force is given by Newton's second law: Net force = mass * acceleration.
Given the mass of the car is 3,000 kg and the acceleration is 3 m/s^2, we have:
Net force = 3,000 kg * 3 m/s^2.
5. Set up the equation for static friction:
The friction force can be calculated using the equation: Friction force = coefficient of friction * normal force.
The normal force is equal to the weight of the car, which we found in step 3.
6. Solve for the coefficient of sliding friction:
Rearrange the equation for friction force to solve for the coefficient of friction:
coefficient of friction = Friction force / normal force.
Now, let's calculate the coefficient of sliding friction:
Step 3: Weight = 3,000 kg * 9.8 m/s^2.
Step 4: Net force = 3,000 kg * 3 m/s^2.
Step 5: Friction force = coefficient of friction * Weight.
Finally, substitute the values into the equation for the coefficient of friction and solve for it:
coefficient of friction = Friction force / Weight.
After performing these calculations, you will find the coefficient of sliding friction between the car and the ground.