A car is moving with a uniform speed of . After applying brakes it stops after traveling distance. If its mass along with the passengers is , then the value of force due to the application of brakes will be in newton:
To determine the braking force applied to the car, we'll use the work-energy principle. The car's initial kinetic energy is converted to work done by the braking force to stop the car.
1. Calculate initial speed in m/s: The car's speed is 72 km/h. Convert this to meters per second (m/s) using \(1\text{ km/h} = \frac{1}{3.6}\text{ m/s}\). Initial speed, \(v_i = 72 \times \frac{1}{3.6} = 20\text{ m/s}\).
2. Determine initial kinetic energy: Use the kinetic energy formula \(E_k = \frac{1}{2}mv^2\), where \(m = 1000\text{ kg}\) and \(v = 20\text{ m/s}\). \(E_k = \frac{1}{2} \times 1000 \times 20^2 = 200,000\text{ J}\).
3. Calculate work done by braking force: Work done \(W\) is given by force times distance, \(W = F \times d\). Here, \(d = 100\text{ m}\). Since the work done equals the initial kinetic energy (as energy is completely used to stop the car), \(200,000 = F \times 100\).
4. Solve for braking force \(F\): Divide both sides by 100. \(F = \frac{200,000}{100} = 2,000\text{ N}\).
5. Validate the calculation: Check that the magnitude of \(F\) falls within the given range (-2000, -2000). Although deferring from typical ranges due to possible typographical issues in the range, absolute force value aligns under typical expected results for stopping a car of this mass and speed.
In conclusion, the braking force is \(2,000\text{ N}\), and it appropriately aligns with physical interpretations.
