A car, mass - 1950 kg, accelerates at +2.33 m/s (squared). Find the magnitude of the normal force acting on the car. If later, when the car is cruising at 26.5 m/s, the driver applies a force of magnitude 10,000 N to stop the car. What is the distance it takes for the car to come to a stop.
On level ground, the "normal force" is the weight, M*g. The force accelerating the car is M*a. It is not clear what they mean by "normal".
For the stopping distance X,
(stopping force)*X = initial kinetic energy
normal reaction=m*g
9.81*1950=19129,5newtons
using the equation of motion:s=[(v^2)-(u^2)]/2a
4,66s=702,25
thus s=150,7m
To find the magnitude of the normal force acting on the car, we need to consider the forces acting on it. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the car is on a flat road, so the normal force will be equal in magnitude and opposite in direction to the gravitational force acting on the car.
1. Calculate the gravitational force acting on the car:
Weight = mass × gravity
Weight = 1950 kg × 9.8 m/s²
Weight = 19110 N
2. The normal force is equal in magnitude and opposite in direction to the weight of the car. Therefore, the magnitude of the normal force is also 19110 N.
To find the distance it takes for the car to come to a stop, we will use the concept of work done by a force. The work done by the driver in stopping the car will be equal to the initial kinetic energy of the car.
1. Calculate the initial kinetic energy of the car:
Kinetic Energy = (1/2) × mass × velocity²
Kinetic Energy = (1/2) × 1950 kg × (26.5 m/s)²
Kinetic Energy = 686,737.5 J
2. The work done by the driver is equal to the change in kinetic energy of the car.
Work = Final Kinetic Energy - Initial Kinetic Energy
Since the car comes to a stop, the final kinetic energy is zero.
Work = 0 - 686,737.5 J
Work = -686,737.5 J
3. The work done by a force is given by the formula: Work = Force × Distance.
Therefore, to find the distance, we rearrange the formula:
Distance = Work / Force
Distance = -686,737.5 J / (-10,000 N)
Distance = 68.67 meters
Therefore, it takes the car a distance of 68.67 meters to come to a stop.