suppose you have 2 cars, and the larger one is twice as massive as the smaller one. If you and a friend push on them so that their accelerations are equal, how must the forces applied to the cars compare?
a. the force on the larger car is equal to that on the smaller car.
b. the force on the larger car is 1/2 that on the smaller car.
c. the force on the larger car is twice that on the smaller car.
d. the force on the larger car is more than three times that on the smaller car.
Using the equation F = m a, you should be able to figure this out.
If the accleration "a" is the same for both cars, what happens to F when m doubles?
gets larger?
Yes, the force must double
To determine how the forces applied to the two cars compare, we can use Newton's second law of motion, which states:
Force = Mass × Acceleration
Let's denote the mass of the smaller car as m1 and the mass of the larger car as m2. Given that the larger car is twice as massive as the smaller one, we can express this relationship as:
m2 = 2m1
Since the accelerations are equal, we can let the acceleration of both cars be represented by the same symbol, a.
Now, let's consider the force applied to the smaller car (F1) and the force applied to the larger car (F2). According to Newton's second law, we have:
F1 = m1 × a
F2 = m2 × a
Substituting the relationship m2 = 2m1 into the equation for F2, we get:
F2 = (2m1) × a
Comparing the equations for F1 and F2, we can see that the force applied to the larger car is twice that on the smaller car:
F2 = 2F1
Therefore, the correct answer is c. The force on the larger car is twice that on the smaller car.