A car of mass 1000 kg is travelling down a steep hill. The brakes fail and the driver uses a horizontal sand-filled safety road to stop the car.The car enters the sand at a speed of 10 m / s and experiences a constant stopping force of 2500 N.How far does the car travel in the sand before coming to rest?
Question
A car of mass 1000 kg is travelling down a steep hill. The brakes fail and the driver uses a horizontal sand-filled safety road to stop the car.The car enters the sand at a speed of 10 m / s and experiences a constant stopping force of 2500 N.How far does the car travel in the sand before coming to rest?
Solution
To solve this problem, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
Step 1: Calculate the initial kinetic energy of the car. The kinetic energy (KE) of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.
KE_initial = 1/2 * 1000 kg * (10 m/s)^2 = 50,000 Joules
Step 2: Calculate the work done by the stopping force. The work done (W) by a force is given by the formula W = F * d, where F is the force and d is the distance over which the force is applied. In this case, we don't know the distance yet, but we know that the work done is equal to the change in kinetic energy of the car.
Since the car comes to rest, its final kinetic energy is 0. Therefore, the work done by the stopping force is equal to the initial kinetic energy of the car.
W = KE_initial = 50,000 Joules
Step 3: Calculate the distance the car travels in the sand. We can rearrange the formula for work to solve for distance: d = W / F.
d = 50,000 Joules / 2500 N = 20 meters
So, the car travels 20 meters in the sand before coming to rest.
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