A 2260kg truck drives East with a constant velocity of 18m/s. It comes to a stop after traveling 123m. What is the noraml force exerted by the road on the truck?
Also, is the distance travelled essential to solve the problem or is unnecessary information?
Well, since the truck comes to a stop, we know that there must be some sort of force acting opposite to the direction of motion. This force is provided by the friction between the tires and the road. The normal force, denoted by N, is the force exerted by the road on the truck perpendicular to the road surface. It is equal in magnitude and opposite in direction to the force of gravity acting on the truck.
Now, regarding the distance traveled, it is actually unnecessary information to solve this particular problem. We can determine the normal force just based on the mass of the truck and its velocity. So, we can go ahead and calculate the normal force without worrying about the distance traveled. You're off the hook, distance!
To solve the problem, we need to determine the normal force exerted by the road on the truck.
The distance traveled by the truck is not essential information for finding the normal force. It is only provided to give context to the problem.
To find the normal force, we can use Newton's second law of motion:
Net force = mass × acceleration
Since the truck comes to a stop, its final velocity is 0 m/s. The initial velocity is 18 m/s. The acceleration can be found using the equation:
Final velocity^2 = Initial velocity^2 + 2 × acceleration × distance
0^2 = 18^2 + 2 × acceleration × 123
0 = 324 + 246 × acceleration
Rearranging the equation, we get:
246 × acceleration = -324
acceleration = -324/246
acceleration ≈ -1.32 m/s^2
Since the truck is moving east and coming to a stop, the net force acting on it is in the opposite direction (west). The only horizontal force acting on the truck is the friction force between the tires and the road.
The normal force (N) exerted by the road on the truck is equal in magnitude but opposite in direction to the weight of the truck. The weight can be calculated using the equation:
Weight = mass × gravity
where gravity ≈ 9.8 m/s^2.
Weight = 2260 kg × 9.8 m/s^2
Weight ≈ 22148 N
So, the normal force exerted by the road on the truck is 22148 N in the upward direction.
To find the normal force exerted by the road on the truck, we need to consider the forces acting on the truck.
First, we can determine the acceleration of the truck using the equation:
a = (vf - vi) / t
Given that the truck comes to a stop (vf = 0), the initial velocity (vi) is 18 m/s, and the time (t) can be calculated using the distance travelled and velocity:
t = d / v
Substituting the given values, we have:
t = 123m / 18m/s = 6.83s
Now, we can calculate the acceleration:
a = (0 - 18m/s) / 6.83s = -2.64 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, i.e., West.
Next, we consider the forces acting on the truck. When the truck comes to a stop, the net force acting on it is in the opposite direction of its initial motion. In this case, it is West.
Since we want to find the normal force exerted by the road, we need to consider gravitational force, which acts vertically downward, and vertical normal force. The normal force counters the gravitational force to keep the truck from sinking into the road.
However, in this problem, assuming a flat road and neglecting any inclined angle, the vertical forces do not affect the horizontal motion. So, we can ignore the distance travelled (123m) when calculating the normal force.
Hence, to solve the problem and find the normal force exerted by the road, we only need to know the mass of the truck. The distance travelled is not essential information for this specific question.