A car (m = 1670 kg) is parked on a road that rises 10.3 ° above the horizontal. What are the magnitudes of (a) the normal force and (b) the static frictional force that the ground exerts on the tires?
Wc = mg = 1670kg * 9.8N/kg = 16,366N. =
Weight of car.
Fc = (16,366N.,10.3 deg.),
Fp = 16,366sin10.3 = 2826.3N. = Force
parallel to plane.
a. Fv = 16,366cos10.3 = 16,102.3N. = Force perpendicular to plane = Normal force.
b. Ff = Force due to friction.
Fn = ma = 0 = Net force, a = 0.
Fn =Fp - Ff = 0,
2826.3 - Ff = 0,
Ff = 2826.3N. = Force of friction.
To find the magnitudes of the normal force and the static frictional force exerted on the tires of the parked car, let's break down the problem step by step.
Step 1: Understanding the scenario
A car is parked on a road that is inclined at an angle of 10.3° with respect to the horizontal.
Step 2: Calculate the weight of the car
The weight of an object is given by the formula:
Weight = mass x acceleration due to gravity
In this case, the mass of the car (m) is given as 1670 kg, and the acceleration due to gravity (g) is approximately 9.8 m/s². Therefore, we can calculate the weight of the car:
Weight = 1670 kg x 9.8 m/s²
Step 3: Decompose the weight into components
Since the road is inclined at an angle, we need to break down the weight of the car into two perpendicular components. The vertical component is called the normal force, and the horizontal component is the force of static friction.
Step 4: Calculate the magnitude of the normal force
The normal force (N) is the force exerted by a surface perpendicular to it. In this case, it is the force exerted by the road to support the weight of the car. The normal force is equal in magnitude but opposite in direction to the vertical component of the weight. Therefore, the magnitude of the normal force is given by:
N = Weight × cos(angle)
Plug in the values to get:
N = (1670 kg × 9.8 m/s²) × cos(10.3°)
Step 5: Calculate the magnitude of the static frictional force
The static frictional force (F_friction) is the force that prevents the car from sliding down the inclined road. It acts parallel to the road surface and opposes any motion. The magnitude of the static frictional force is given by:
F_friction = Weight × sin(angle)
Plug in the values to get:
F_friction = (1670 kg × 9.8 m/s²) × sin(10.3°)
Step 6: Calculate and round the final values
Use a calculator to evaluate the expressions above and round the results to the appropriate number of significant figures. The final magnitudes of the normal force and static frictional force can then be obtained.
Please note that in this explanation, we have assumed that there is no vertical acceleration and the car is in equilibrium.