Question

Two plastic projectiles have the same mass M and speed V when they hit a glass window pane at a right angle. The interaction between both projectiles and the glass pane takes time T. Projectile A bounces off of the window (in the opposite direction) with the same speed V it had at the beginning. Projectile B sticks to the window pane and stops. Describe the likely damage to the glass pane by selecting all the true statements below.

a. Projectile B has the greater likelihood of breaking the glass since its final momentum is smaller
b. Projectiles A & B have the same likelihood of breaking the glass since they have the same initial momentum
c. Projectile A has the greater likelihood of breaking the glass since its momentum change is larger
d. Projectile A has the greater likelihood of breaking the glass since its momentum change is smaller

Answer 1

b. Projectiles A & B have the same likelihood of breaking the glass since they have the same initial momentum

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c. Projectile A has the greater likelihood of breaking the glass since its momentum change is larger.

Step-by-step explanation:

for option b, the two projectiles have the same initial mass and velocity, hence they posses the same amount of momentum that if sufficient enough could break the glass.

for option c, projectile A changes direction, maintaining the same speed v. Its momentum changes from from mv to -mv, since its speed changed direction.

the difference in momentum becomes

Δp = -mv - mv = -2mv

this is twice the initial momentum.

projectile B changes momentum from mv to 0

Δp = 0 - mv = -mv.

this is half of the final momentum of projectile A.

Also we know that force is proportional to to the rate of change of momentum, which is greater in projectile A, therefore projectile A impacts more force on the glass. Projectile A therefore has the greater likelihood of breaking the glass since its momentum change is larger.