A driver of a 7100 N car passes a sign stating "Bridge Out 30 Meters Ahead." She slams on the brakes, coming to a stop in 10 s. How much work must be done by the brakes on the car if it is to stop just in time? Neglect the weight of the driver, and assume that the negative acceleration of the car caused by the braking is constant.
A car slams on its brakes, coming to a complete stop in 4.0 s. The car was traveling south at 60.0 mph. Calculate the acceleration.
mi/h/s
To find the work done by the brakes in stopping the car, we need to determine the change in kinetic energy of the car. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
Here's how you can find the answer:
1. Determine the initial velocity of the car.
We can use the equation: v = u + at, where v is the final velocity (zero since the car comes to a stop), u is the initial velocity, a is the acceleration, and t is the time taken to stop (10 s in this case).
Rearranging the equation to solve for u, we get: u = v - at.
Substituting the given values: u = 0 - (7100 N / mass of the car) × 10 s.
2. Calculate the mass of the car.
We know the weight of the car, which is 7100 N. The weight of an object can be calculated using the equation: weight = mass × gravitational acceleration.
Rearranging the equation to solve for mass, we get: mass = weight / gravitational acceleration.
Substituting the given values: mass = 7100 N / 9.8 m/s^2.
3. Determine the change in kinetic energy.
The kinetic energy of an object can be calculated using the equation: kinetic energy = 0.5 × mass × velocity^2.
Initially, the kinetic energy is 0. At the end, when the car comes to a stop, the kinetic energy is also 0.
Therefore, the change in kinetic energy is 0 - 0 = 0.
4. Calculate the work done by the brakes.
Since the change in kinetic energy is 0, the work done by the brakes to stop the car is also 0.
Therefore, the work done by the brakes on the car in order to stop just in time is 0.