Suppose a 10,000 kg truck collides with a 1,000 kg car. During the collision, is the force of the truck on the car...

Question

1) Suppose a 10,000 kg truck collides with a 1,000 kg car. During the collision, is the force of the truck on the car...

A) greater than the force of the car on the truck

B) less than the force of the car on the truck

C) equal to the force of the car on the truck

D) no way to determine

E) none of the above

2) In the previous question, how do the accelerations felt by the drivers of the truck and car compare?

A) truck driver feels larger acceleration

B) car driver feels larger acceleration

C) both drivers feel equal accelerations

D) no way to determine

E) none of the above

Answer 1

This problem is about the conservation of momentum. Momentum is the product of mass and velocity: P = m*v

We have the masses for the 2 objects. After they collide, they will b moving with a new velocity which give the same total momentum. The new momentum is the sum of the momentums before the collision. Let's write the expressions:

vi = initial velocity

vf = final velocity

pi = initial momentum

for the car:

pi_c = 1000*vi_c

for the truck:

pi_t = 10000*vi_t

pf = final momentum = sum of initial momentum = 1000*vi_c+10000*vi_t

_{But, the final velocity is the same for both car and truck, so now we have :}

_{pf = 11000* vf}

_{We can see that the final momentum is dominated by the mass of the truck---thus its velocity does not change nearly as much as doe the velocity of the car.....now we can answer the first questions:}

the car experiences the largest change in velocity, and therefor the most acceleration. This means the force on the car is higher because of acceleration, but this is moderated by the difference in masses. An additional calculation is required to get the exact effect.

The second question is easier....the car, having lower mass, has higher acceleration in the collision, meaning the driver experiences higher acceleration---relative to the car

Answer 2

1) Suppose a 10,000 kg truck collides with a 1,000 kg car. During the collision, is the force of the truck on the car...

Due to Newton's third law (if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A), both forces will be equal.

Correct answer: C) equal to the force of the car on the truck

2) In the previous question, how do the accelerations felt by the drivers of the truck and car compare?

force = mass * acceleration

Since the truck and the car both experience the same force, the car with less mass will experience a larger acceleration and the truck with more mass will experience a smaller acceleration.

Correct answer: B) car driver feels larger acceleration