Question

The coefficient of friction between the wheels of Yamaha motorcycle and the dry pavement is 0.88. An animal walks out into the road, causing a motorcyclist to slam on the brakes. The wheels stop turning, but the tires skid along the road, causing intense friction and heat.

Determine the magnitude (positive) of the acceleration which the 196-kg motorcycle experiences while skidding to a stop. The mass includes the rider.
Answer: ____ m/s/s (or m/s^2)

Answer 1

The motorcycle, including the rider with a total mass of 196 kg and a coefficient of friction of 0.88 with dry pavement, experiences an acceleration of 8.65 m/s^2 while skidding to a stop due to friction.

Step-by-step explanation:

To determine the magnitude of the acceleration experienced by the 196-kg motorcycle while skidding to a stop, we use Newton's second law of motion and the fact that the force of friction is the only horizontal force acting on the motorcycle once it starts skidding.

The force of friction (Ffriction) can be calculated using the formula:

Ffriction = μ * m * g,

where μ is the coefficient of friction, m is the mass of the motorcycle including the rider, and g is the acceleration due to gravity (approximated to 9.81 m/s2). Substituting the given values:

Ffriction = 0.88 * 196 kg * 9.81 m/s2 = 1695.63 N.

To find the acceleration (a), we apply Newton's second law:

F = m * a,

where the force of friction is the force (F) acting on the motorcycle to decelerate it. So:

a = Ffriction / m,

a = 1695.63 N / 196 kg = 8.65 m/s2.

The motorcycle experiences an acceleration of 8.65 m/s2 opposite to the direction of motion while skidding to a stop.

Answer 2

To determine the magnitude of the acceleration of the motorcycle, we need to know the force of friction acting on the wheels. The force of friction is equal to the coefficient of friction multiplied by the normal force acting on the wheels, which is equal to the weight of the motorcycle and rider. The weight of the motorcycle and rider can be calculated by multiplying the mass by the acceleration due to gravity (9.8 m/s^2). So, the force of friction acting on the wheels of the motorcycle is equal to 0.88 * 196 kg * 9.8 m/s^2 = 1661.28 N.

The acceleration of the motorcycle is equal to the force of friction divided by the mass of the motorcycle and rider. So, the acceleration of the motorcycle is equal to 1661.28 N / 196 kg = 8.45 m/s^2.

Answer: 8.45 m/s^2