Muhammad A. answered • 02/25/23
Refreshing Ideas, Broadening Visions
(a)
To find how high a hill the car can coast up, we need to use the conservation of energy principle, which states that the initial energy of the car (kinetic energy) is equal to the final energy of the car (potential energy). Assuming negligible friction, we can write:
1/2 mv^2 = mgh
where m is the mass of the car, v is the initial velocity, g is the acceleration due to gravity, and h is the height of the hill.
Substituting the given values, we have:
1/2 (1000 kg) (92.0 km/h)^2 = (1000 kg) g h
Solving for h, we get:
h = (1/2) [(92.0 km/h)^2 / g] = 400 m (approx)
Therefore, the car can coast up a hill with a height of approximately 400 meters.
(b)
To find the thermal energy generated by friction, we can use the work-energy principle, which states that the work done by friction is equal to the change in kinetic energy of the car. Since the car comes to a stop at the end of its motion, the initial kinetic energy is equal to the final kinetic energy, which is zero. Thus, the work done by friction is equal to the initial kinetic energy. We can write:
W = 1/2 mv^2
where W is the work done by friction.
Substituting the given values, we have:
W = 1/2 (750 kg) (92.0 km/h)^2 = 2.54 × 10^7 J (approx)
Therefore, the thermal energy generated by friction is approximately 2.54 × 10^7 J.
(c)
To find the average force of friction, we can use the formula:
Ff = mg sinθ
where Ff is the force of friction, m is the mass of the car, g is the acceleration due to gravity, and θ is the angle of the slope.
Substituting the given values, we have:
Ff = (750 kg) (9.81 m/s^2) sin 2.5° = 32.8 N (approx)
Therefore, the average force of friction is approximately 32.8 N.
