Calculating Speed of a Rolling Cart with Added Mass and Running Man

However, in this case, we are only considering the momentum of the cart itself as it is the object we are interested in finding the speed of. Therefore, we do not include the man's momentum in our calculation.
  • #1
ElectricMile
31
0
A 1000 kg cart is rolling to the right at 1.70m/s . A 70.0 kg man is standing on the right end of the cart.What is the speed of the cart if the man suddenly starts running to the left with a speed of 7.00 m/s relative to the cart?


really boggles my mind, should i be using

=(m1 +m2)Vf - m1(Vi)/m2
or what's going on?!
 
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  • #2
(m1+m2)vb=m1*v1a+m2*v2a
we put the positive direction as right
(m1+m2)vb/m1-m2*v2a/m1=v1a

Im not sure how you define the masses but i think you missed (m1 +m2)Vf/!m2!
 
  • #3
Conservation of momentum. Initially, the 1000kg cart is rolling to the rightare 1.7 m/s while the man is standing still, so the total momentum is (mass)(velocity) 1700 kgm/s.

Let v be the speed of the cart after the man starts running. When the man (mass 70.0 kg) runs to the right at 7.00 m/s, relative to the cart, his speed relative to the ground is v- 7 and so his momentum, relative to the ground, is 70(v- 7)= 70v- 490 kgm/s. The momentum of the cart is 1000v and so the total momentum is now
1070v- 490 . By conservation of momentum, that must be
1070v- 490= 1700=> 1070v= 2190 so v= 2190/1070= 2.05 m/s to the right.
 
  • #4
Isn't the initial momentum a result of the mass of both the cart and the man, 1070 x1.7 or 1819 to the right ? If so, leads to 2.15 m/s
 
  • #5
regor60 said:
Isn't the initial momentum a result of the mass of both the cart and the man, 1070 x1.7 or 1819 to the right ?
Yes, the initial momentum must include the man moving with the cart.
 

What is a rolling cart?

A rolling cart is a type of utility cart that has wheels on the bottom, allowing it to be easily moved from one place to another. It is typically used for transporting items or materials in various settings such as offices, warehouses, and hospitals.

What are the different types of rolling carts?

There are several types of rolling carts, including service carts, platform carts, hand trucks, and utility carts. Service carts are typically used for serving food or drinks, while platform carts are used for moving larger items. Hand trucks are designed for heavy lifting, and utility carts are versatile and can be used for various purposes.

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What are the benefits of using a rolling cart?

Rolling carts offer several benefits, including increased efficiency, convenience, and organization. They can save time and effort by allowing you to transport multiple items at once instead of making multiple trips. They also keep items organized and easily accessible, reducing clutter and improving workflow.

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To choose the right rolling cart, you should consider the weight and size of the items you need to transport, the terrain and environment the cart will be used in, and the features you require such as shelves, drawers, or handles. It is also essential to consider the material and durability of the cart to ensure it can withstand your intended use.

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