Physics Review Question

**Unit:** mechanics

**Year:** 1995 **Question#:** 14

**Question:** In the diagram below, a 0.4-kilogram steel sphere
and a 0.1-kilogram wooden sphere are located 2.0 meters above the ground.
Both spheres are allowed to fall from rest.

Which statement best describes the spheres after they have fallen 1.0 meter?
[neglect air resistance.]

(1* *) Both spheres have the same speed and
momentum.

(2* *) Both spheres have the same speed and
the steel sphere has more momentum than the wooden sphere.

(3* *) The steel sphere has greater speed
and has less momentum that the wooden sphere.

(4* *) The steel sphere has greater speed
than the wooden sphere and both spheres have the same momentum.

What is this question really asking?* *

Explanation by: Gabrielle

[ Return to question menu* *]

**Answer 1**

Both spheres have the same speed and momentum

INCORRECT

Use the formula Vf^{2}=Vi^{2} + 2a s to figure out the speed
of the objects. You will find that the speed of the steel ball and the speed
of the wood ball are equal. To find the momentum use the formula p=mv. You
will find that the momentums are not the same. return to
top* *

**Answer 2**

Both spheres have the same speed and the steel sphere has more momentum
than the wooden sphere.

CORRECT

Use the formula Vf^{2} = Vi^{2} + 2a s to find the speed
of the objects. Vi= 0m/s, a=9.8m/ss, s=1m. Vf^{2}=0m/s^{2}+2(9.8m/ss)(1m)=
m/s. The objects have the same velocity because no conditions of
the formula differ. To find the momentum use the formula p=mv. For the steel
ball mass=.4kg and the velocity=m/s. P=(.4kg)(m/s). P=1.7kg*m/s.
For the wood ball mass=.1 kg, velocity=m/s. P=(.1kg)(m/s). P=.44Kg*m/s.
The momentum of the steel ball is greater than that of the wood ball. They
have the same speed but different momentums. return to top*
*

**Answer 3**

The steel sphere has greater speed and has less momentum that the wooden
sphere.

INCORRECT

The two balls have the same speed and the steel ball has more momentum than
the wooden ball. return to top* *

**Answer 4**

The steel sphere has greater speed than the wooden sphere and both spheres
have the same momentum.

INCORRECT

Ignoring air friction, all objects fall at the same rate (acceleration due
to gravity) so the speed of the objects both dropped at the same time could
not be different. The momentum (p=mv) would be different for each because
the mass is different.

return to top* *

**What's this question really asking?**

This question is really asking under what conditions are the momentums of
two different objects different (when the mass is different and/or the velocity)
and without air resistance are the speeds of two objects the same.