Question

You are driving your 1700 kg car at 22 m/s down a hill with a 5.0° slope when a deer suddenly jumps out onto the roadway. You slam on your brakes, skidding to a stop. Part A How far do you skid before stopping if the kinetic friction force between your tires and the road is 1.2x104 N ? Solve this problem using conservation of energy. Express your answer with the appropriate units. MÅ ? d = Value Units

Answer 1

The car will skid for approximately 100.3 meters before coming to a stop.

Step-by-step explanation:

To determine how far you skid before stopping, we can use the principle of conservation of energy. The initial kinetic energy is converted into work done by the friction force. The work done by the friction force can be calculated as the product of the force of friction and the distance over which it acts.

The work done by the friction force is equal to the change in kinetic energy. At the initial velocity, the kinetic energy is given by 1/2 mv^2, where m is the mass of the car and v is the initial velocity. At the final velocity of 0 m/s, the kinetic energy is 0. Therefore, the work done by the friction force is equal to the initial kinetic energy.

The work done by the friction force can be calculated as W = Fd, where W is the work done, F is the force of friction, and d is the distance over which the force of friction acts. Solving for d, we get d = W/F. Substituting the values into the equation, we have d = (1/2)mv^2 / F.

Plugging in the values, we have d = (1/2)(1700 kg)(22 m/s)^2 / (1.2x10^4 N) = 100.3 m.

Answer 2

To determine the distance the car will skid to a stop, conservation of energy is used. The initial kinetic energy is set equal to the work done by the kinetic friction force. Solving for the distance yields a skid of 3.12 meters.

Step-by-step explanation:

To solve this problem using the conservation of energy, we first note that the initial kinetic energy of the car is converted into work done by friction as the car skids to a stop. The initial kinetic energy (KE) is given by ½ mv², where m is the mass of the car and v is its initial velocity. The work done by the friction force (Fk) over the distance d that the car skids is given by Fkd. Setting these equal to each other gives us:

½(1700 kg)(22 m/s)² = (1.2 x 10⁴ N)d

Solving for d gives us:

d = ½(1700 kg)(22 m/s)² / (1.2 x 10⁴ N)

d = (37400 J) / (1.2 x 10⁴ N)

d = 3.12 m

The car will skid to a stop over a distance of 3.12 meters. Note that we assumed no energy loss other than what's due to kinetic friction and neglected the gravitational component along the hill's slope for simplification.