A 2.284 km car is moving down a road with a slope of 13% at a constant speed of 11 m/s. What is the direction and magnitude of the frictional force?
To determine the direction and magnitude of the frictional force acting on the car, we can break down the problem into different components.
First, let's find the gravitational force acting on the car. The gravitational force can be calculated using the formula:
Force_gravity = mass * gravity
where mass is the mass of the car and gravity is the acceleration due to gravity (approximately 9.8 m/s^2). However, the mass of the car is not given in the problem, so we cannot calculate the exact gravitational force.
Next, let's find the force component acting parallel to the slope. This force component can be calculated using the formula:
Force_parallel = mass * acceleration_parallel
Since the car is moving at a constant speed, the acceleration parallel to the slope is zero. Therefore, the force component acting parallel to the slope is also zero.
Now, let's calculate the force component acting perpendicular to the slope. This force component is responsible for opposing the gravitational force. The force component perpendicular to the slope can be calculated using the formula:
Force_perpendicular = mass * acceleration_perpendicular
where the acceleration perpendicular can be determined using the slope angle and the gravitational acceleration.
The slope angle (θ) can be calculated using the formula:
θ = arctan(slope)
In this case, the slope is given as 13%. Plugging the value into the formula, we have:
θ = arctan(0.13) ≈ 7.46 degrees
Now that we have the slope angle, we can find the acceleration perpendicular. The acceleration perpendicular (a_perpendicular) is given by the formula:
a_perpendicular = gravity * sin(θ)
Plugging in the values, we have:
a_perpendicular = 9.8 * sin(7.46) ≈ 0.90 m/s^2
Finally, we can calculate the force component acting perpendicular to the slope:
Force_perpendicular = mass * acceleration_perpendicular
However, since the mass of the car is not given, we cannot calculate the exact force value.
Given that the car is moving at a constant speed of 11 m/s, we can deduce that the frictional force acting on the car must be equal in magnitude but opposite in direction to the force component acting parallel to the slope.
Therefore, the direction of the frictional force is opposite to the direction of motion, and its magnitude would be equal to the mass of the car times the acceleration parallel, which is zero in this case. Thus, the magnitude of the frictional force is zero, and it acts in the opposite direction to the car's motion.