A car of mass m traveling at a velocity of 20m/s east on a straight level road and a truck of mass 2m travelling at 20m/s west on the same road. ignore the effects of friction.
calculate the velocity of the truck-car system immediately after collision.
On impact the car exerts a force of magnitude F on the truck and experiences an acceleration of magnitude a.
Determine, in terms of F, the magnitude of the force that the truck exerts on the car on impact and in terms of a, the acceleration that the truck experiences on impact.
Newtons third law:
Force a truck exerts on the car is -F (opposite direction from F).
Acceleration is -a/2 :(due to twice mass).
To determine the velocity of the truck-car system immediately after collision, we can consider the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
Given:
Mass of the car = m
Velocity of the car = 20 m/s (east)
Mass of the truck = 2m
Velocity of the truck = 20 m/s (west)
Let's consider the direction towards the east as positive and towards the west as negative.
The initial momentum of the car is given by:
P_initial_car = m * V_car
= m * (20 m/s)
The initial momentum of the truck is given by:
P_initial_truck = (2m) * V_truck
= (2m) * (-20 m/s) (negative since it's in the opposite direction)
According to the law of conservation of momentum:
P_initial_car + P_initial_truck = P_final_car + P_final_truck
Therefore,
m * (20 m/s) + (2m) * (-20 m/s) = P_final_car + P_final_truck
Plugging in the given values, we can simplify it to:
20m - 40m = P_final_car + P_final_truck
-20m = P_final_car + P_final_truck
Now, let's consider the forces and accelerations involved.
The force exerted by the car on the truck, F, causes the car to experience an acceleration, a.
According to Newton's second law of motion, the force applied to an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
Since the truck exerts an equal and opposite force on the car (due to Newton's third law of motion), the force exerted by the truck on the car is also F.
Similarly, the acceleration experienced by the truck, a_truck, would be the same magnitude but in the opposite direction.
So, the force exerted by the truck on the car is F, and the acceleration of the truck is -a.
To summarize:
Magnitude of the velocity of the truck-car system immediately after the collision: 0 m/s (since they are moving with the same speed in opposite directions)
Magnitude of the force that the truck exerts on the car on impact: F
Magnitude of the acceleration that the truck experiences on impact: -a