A car which has a mass of 1.36 tonnes is travelling at 26.8m/s on a level road when the driver brings the car to an emergency stop using only the brakes. A time interval of 4.18s is required to bring the car to a stop.
Calculate the braking force acting on the car while the car comes to a stop.
To calculate the braking force acting on the car, you can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). In this case, the acceleration is due to the deceleration caused by braking.
First, convert the mass of the car from tonnes to kilograms. Since 1 tonne is equal to 1000 kilograms, the mass of the car is:
mass = 1.36 tonnes × 1000 kg/tonne = 1360 kg
Next, find the acceleration of the car using the formula:
acceleration = (final velocity - initial velocity)/time
The initial velocity (u) is 26.8 m/s, the final velocity (v) is 0 m/s (since the car comes to a stop), and the time interval (t) is 4.18 s. Substituting these values into the formula:
acceleration = (0 m/s - 26.8 m/s)/4.18 s
Simplifying:
acceleration = -26.8 m/s / 4.18 s
acceleration ≈ -6.41 m/s²
The negative sign indicates that the car is decelerating.
Finally, calculate the braking force using Newton's second law:
force = mass × acceleration
Substitute the mass and acceleration values into the formula:
force = 1360 kg × -6.41 m/s²
Calculating,
force ≈ -8723.6 N
The negative sign indicates that the force is acting in the opposite direction of the car's motion. Hence, the braking force acting on the car is approximately -8723.6 Newtons.