7. A 1800 kg car drives up an inclined of 8% from rest at uniform acceleration to a velocity of 60 kph after traveling 75 m. Its wheels are 3 m apart with its center of gravity midway of the wheels and 500 mm from the ground. If all frictional force is assumed to act at the rear wheels.
A. Which of the following gives the acceleration of the car.
B. Which of the following gives the normal force on front wheels.
C. Which of the following gives the minimum coefficient of friction needed so that motion is possible.
8. An auto, equipped only front wheel brakes, has a wheelbase of 3 m with its c.g. located 1.50 m ahead of the rear wheels and 0.90 m above the pavement. If μK = 0.80 at the tires, compute the minimum distance in which the auto can be brought to rest from a speed of 90 kph, if the driver’s reaction time before applying the brakes is 3/4 second.
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OKAY
A. Sorry, I can't solve that one for you. My brain is made of rubber, not calculus.
B. The normal force on the front wheels depends on how much they've been working out. Have they been hitting the gym lately?
C. The minimum coefficient of friction needed is "just enough." Just like when you're trying to impress your crush with a joke - you don't want to be too cheesy, but you also want to have a little bit of a grip.
8. Whoa, slow down! I can't handle all these numbers. I'm more of a clown than a mathematician. But hey, have you heard the joke about the car and the banana peel? It's a real slip-up!
To solve these types of physics problems, we can use the concepts of force, acceleration, friction, and motion equations. Let's break down each question step by step:
7. A. To find the acceleration of the car, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (60 km/h)
u = initial velocity (0 m/s)
a = acceleration (unknown)
s = displacement (75 m)
First, we need to convert the final velocity from km/h to m/s:
60 km/h = 60 * (1000 m / 3600 s) ≈ 16.67 m/s
Now, we can rearrange the equation to solve for the acceleration:
a = (v^2 - u^2) / (2s)
a = (16.67^2 - 0) / (2 * 75)
a ≈ 5.556 m/s^2
Therefore, the acceleration of the car is approximately 5.556 m/s^2.
7. B. To find the normal force on the front wheels, we need to consider the forces acting on the car. The normal force is the force exerted perpendicular to the surface by the object resting on it (in this case, the car). Since the car is on an inclined plane, the normal force can be calculated using the following formula:
Normal force = mg * cosθ
Where:
m = mass of the car (1800 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
θ = angle of the incline (given as 8%)
First, we need to find the angle in radians:
θ = 8% = 8 / 100 = 0.08 radians
Now, we can calculate the normal force:
Normal force = 1800 * 9.8 * cos(0.08)
Normal force ≈ 17294.66 N
Therefore, the normal force on the front wheels is approximately 17294.66 N.
7. C. To find the minimum coefficient of friction needed for motion to be possible, we need to consider the forces acting on the car. The coefficient of friction (μ) is a dimensionless constant that represents the interaction between two surfaces. In this case, we want to find the minimum value of μ to keep the car from sliding backward.
The force of friction (Ff) can be calculated using the following formula:
Ff = μ * mg
Where:
Ff = force of friction
μ = coefficient of friction (unknown)
m = mass of the car (1800 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
Since all the frictional force is assumed to act at the rear wheels, we need to find the weight distribution on the rear wheels to determine the minimum coefficient of friction.
Rear wheel weight (Wr) = (m * g) / 2
Wr = (1800 * 9.8) / 2
Wr ≈ 8820 N
Now, we can calculate the minimum coefficient of friction:
μ_min = Ff / Wr
μ_min = (μ * m * g) / Wr
Considering that the car is on an incline, the minimum coefficient of friction occurs when the car is about to slip backward (when the force of friction is at its maximum). This occurs when the friction force is equal to the maximum value of μ times the normal force on the rear wheels.
Ff_max = μ_max * Wr
Therefore, to find the minimum coefficient of friction (μ_min), we can substitute this equation into the earlier equation:
μ_min = (Ff_max / Wr) = (μ_max * Wr / Wr) = μ_max
Since μ_min is the minimum coefficient of friction when motion is just possible, the answer to Option C is μ_min.