A 1300-kg car moving on a horizontal surface has speed v=65 km/h when it strikes a horizontal coield spring and is brought to rest in a distance of 3.0m
To find the force exerted by the coiled spring on the car, we can use the equation for work done by a force:
Work = Force x Distance
Since the car is brought to rest, the work done by the spring is equal to the initial kinetic energy of the car:
Work = Kinetic Energy
The initial kinetic energy of the car can be calculated using the equation:
Kinetic Energy = (1/2) x mass x velocity^2
Given:
Mass of the car, m = 1300 kg
Velocity of the car, v = 65 km/h (which needs to be converted to m/s)
First, let's convert the car's velocity from km/h to m/s:
Velocity (m/s) = Velocity (km/h) x (1000 m/1 km) x (1 h/3600 s)
Plugging in the values:
Velocity (m/s) = 65 km/h x (1000 m/1 km) x (1 h/3600 s)
Velocity (m/s) = 18.06 m/s (approx.)
Now, we can calculate the initial kinetic energy of the car:
Kinetic Energy = (1/2) x mass x velocity^2
Kinetic Energy = (1/2) x 1300 kg x (18.06 m/s)^2
Kinetic Energy = 214,359 J (approx.)
Since work is equal to kinetic energy, we can say:
Work = 214,359 J
Next, we need to find the force exerted by the spring. Given that the distance is 3.0 m, we can calculate the force:
Work = Force x Distance
214,359 J = Force x 3.0 m
Solving for Force:
Force = 214,359 J / 3.0 m
Force = 71,453 N (approx.)
Therefore, the force exerted by the coiled spring on the car is approximately 71,453 Newtons.