A car of mass 1000 kg moving with the velocity of 40 kg per hour collide with a tree and comes to stop in five seconds.calculate the force exerted by the car on the tree.
vf^2=vi^2 + 2*acceleration*distance
where distance= avgvelocity*time= 20*5
aolve for acceleration
then
force= mass*acceleration
To calculate the force exerted by the car on the tree, we can use Newton's second law of motion, which states that force equals mass multiplied by acceleration. In this case, the acceleration can be calculated using the initial velocity, final velocity, and time taken for the car to come to a stop.
First, let's convert the initial velocity from km/h to m/s:
40 km/h * (1,000 m/1 km) * (1 h/3600 s) = 40 * (1,000/1) * (1/3600) = 40000/3600 ≈ 11.11 m/s
Now we can calculate the acceleration using the formula:
Acceleration (a) = (Final velocity - Initial velocity) / Time
Since the car comes to a stop, the final velocity is 0 m/s. The time taken for the car to come to a stop is given as 5 seconds.
Acceleration = (0 - 11.11) / 5 = -11.11 / 5 ≈ -2.22 m/s²
Now let's calculate the force exerted by the car on the tree using Newton's second law:
Force (F) = Mass (m) * Acceleration (a)
Given that the mass of the car is 1000 kg, we can substitute these values into the formula:
Force = 1000 kg * (-2.22 m/s²) = -2220 N
Therefore, the force exerted by the car on the tree is approximately 2220 Newtons. Note that the negative sign indicates that the force is in the opposite direction of the initial motion, which is expected as the car comes to a stop.