Momentum: Find Height to Receive Same Output for Mass m/2

In summary, a stone of mass 1.98 would have the same momentum upon striking the ground as a stone of mass 2.
  • #1
Cole07
106
0

Homework Statement


A stone of mass 'm' is dropped from rest at a height of 1.98 m. From what height would a stone of mass 'm/2' have to be dropped to have the same momentum upon striking the ground?



Homework Equations



?

The Attempt at a Solution



i don't understand 'm/2' doesn't this mean the first mass divided by 2 and so could i not just simple divide1.98 by 2?
 
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  • #2
this is probably the simplest question on this assignment and i don't get it:cry:
 
  • #3
Cole07 said:

Homework Statement


A stone of mass 'm' is dropped from rest at a height of 1.98 m. From what height would a stone of mass 'm/2' have to be dropped to have the same momentum upon striking the ground?



Homework Equations



?

The Attempt at a Solution



i don't understand 'm/2' doesn't this mean the first mass divided by 2 and so could i not just simple divide1.98 by 2?
No. The second mass has half the mass of the first mass. What is the momentum of the first ? You'll need to find its speed.Then proceed to work on the momentum of the second mass.
 
  • #4
how do i do that though if i don't have any number for mass the only number i have is the height of 1.98 m i wasnot given any other numbers?
 
  • #5
Cole07 said:
how do i do that though if i don't have any number for mass the only number i have is the height of 1.98 m i wasnot given any other numbers?
use m for the mass of mass1, and use m/2 for the mass of mass 2. That will work. Now you have a distance but not a speed. Use one of your motion equations from kinematics that solves for the speed as a function of the height. Are you familiar with these equations?
 
  • #6
ok can i use the formula v=square root of 2(9.8)(1.98) ?
and then i need to solve for the mass but i don't recall an equation i can use to find mass since i don't have momentum
 
  • #7
by the way, if one rock has half the mass of the other, how should its speed relate to the other to have the same momentum?
 
  • #8
i was thinking that its speed would be less because it is lighter?
 
  • #9
Cole07 said:
ok can i use the formula v=square root of 2(9.8)(1.98) ?
and then i need to solve for the mass but i don't recall an equation i can use to find mass since i don't have momentum
Yes for the velocity of the first mass. You don't have to solve for the mass. It is given. the mass is 'm'.
Its momentum is m(sq rt of (2)(9.8)(1.98)). Now what speed must the second mass have (which has a mass of m/2) to have the same momentum? Then work backwards to find its height from which it must be dropped to attain that speed.
 
  • #10
ok i got is 7.920000002m

THANK YOU!
 

1. What is momentum?

Momentum is a physical quantity that describes the amount of motion an object has. It is calculated by multiplying an object's mass by its velocity.

2. How is momentum conserved?

Momentum is conserved in a closed system, meaning that the total momentum before an interaction or event is equal to the total momentum after the interaction or event. This is known as the law of conservation of momentum.

3. How does mass affect momentum?

Mass directly affects the momentum of an object. The larger the mass, the more momentum an object will have at a given velocity. This means that objects with greater mass require more force to change their momentum.

4. What is the relationship between momentum and velocity?

Momentum and velocity are directly proportional to each other. This means that if the velocity of an object increases, its momentum will also increase. Similarly, if the velocity decreases, the momentum will also decrease.

5. How can you find the height to receive the same output for mass m/2?

To find the height to receive the same output for mass m/2, you can use the equation for conservation of momentum (m1v1 = m2v2) and solve for the height by setting the initial mass (m1) and velocity (v1) to the original values and the final mass (m2) and velocity (v2) to half of the original values. This will give you the height at which the object will have the same momentum output.

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