A 1000-kg car whose motor delivers a maximum power of 40.0 hp to its wheel can maintain a steady speed of 130 km/h on a horizontal roadway. How large is the friction force that impedes its motion at this speed? Show the solution and answer
To find the friction force that impedes the motion of the car at a speed of 130 km/h, we need to consider the forces acting on the car.
The key concept to understand is that at a steady speed, the net force on the car is zero. This means that the sum of all the forces acting on the car is balanced.
Let's break down the forces acting on the car:
1. The force of gravity (weight): This force is acting vertically downwards and can be calculated using the formula: weight = mass × acceleration due to gravity (g). In this case, the mass of the car is 1000 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the car is weight = 1000 kg × 9.8 m/s^2.
2. The force of friction: This force is acting horizontally opposite to the direction of motion. It is the force that impedes the car's motion. The friction force can be calculated using the formula: friction force = (power output of the motor) / (speed of the car).
Now, let's calculate the friction force:
1. Calculate the weight of the car:
weight = 1000 kg × 9.8 m/s^2 = <<1000*9.8=9800>>9800 N
2. Convert the speed of the car from km/h to m/s:
130 km/h × (1000 m/1 km) × (1 h/3600 s) = (130 × 1000)/(3600) m/s
3. Calculate the friction force:
friction force = (40.0 hp × 746 W/hp) / ((130 × 1000)/(3600) m/s)
Simplifying the above equation will give you the value of the friction force in Newtons, as that is the unit in the SI system.
So, by using the given values and calculations, you can find the value of the friction force that impedes the car's motion at a speed of 130 km/h.