A 0.200 kg plastic cart and a 22.0 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forwards for a time of 1 s, starting from rest. After the force is removed at t = 1s, how does the momentum of the two carts compare?
Question
A 0.200 kg plastic cart and a 22.0 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forwards for a time of 1 s, starting from rest. After the force is removed at t = 1s, how does the momentum of the two carts compare?
Solution 1
The momentum of an object is given by the product of its mass and velocity (p = mv).
Since equal forces are applied to both carts for the same amount of time, they will both experience the same change in momentum (Δp = FΔt). This is due to Newton's second law of motion, which states that the rate of change of momentum of a body is directly proportional to the force applied and occurs in the direction in which the force is applied.
However, because the carts have different masses, they will not have the same final velocities after the force is applied. The lighter plastic cart will have a higher final velocity than the heavier lead cart.
Therefore, even though both carts experience the same change in momentum, the final momentum of the two carts will not be the same. The plastic cart will have a greater momentum because it has a higher velocity, despite its smaller mass.
Solution 2
The momentum of an object is given by the product of its mass and velocity (p=mv). Since the same force is applied to both carts for the same amount of time, they will both experience the same change in momentum (Δp=FΔt), according to Newton's second law.
However, because the lead cart has a much larger mass than the plastic cart, it will have a much smaller change in velocity for the same change in momentum. This is because velocity is inversely proportional to mass when momentum is held constant (v=p/m).
Therefore, after the force is removed, the plastic cart will be moving much faster than the lead cart. However, because the lead cart is much heavier, it will have a larger momentum. This is because even though its velocity is lower, the product of its mass and velocity (its momentum) is larger due to its much larger mass.
In conclusion, the lead cart will have a larger momentum than the plastic cart after the force is removed.
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