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IceJOKER [234]
3 years ago
6

A 1-pound ball and a 100-pound ball are dropped from a height of 10 feet at the same time. in the absence of air resistance, ___

_______.
Physics
2 answers:
Elena L [17]3 years ago
7 0
The 100 ball would fall faster
professor190 [17]3 years ago
6 0

Answer:

They both will reach the ground at the same time. it will be a tie

Explanation:

Given

m_1 = 1 lb\\\\m_2 = 100 lb\\\\height,h = 10 ft\\\\

Known

acceleration due to gravity,g = 32.2 ft/s^2\\

Solution

Since the balls are dropped freely, their inital velocity u is zero.

let us find the final velocity of 1 pound ball

v^2=-u^2 + 2gh\\\\v^2 = 0^2 + 2 \times 32.2 \times 10\\\\v^2 = 196\\\\v = 25.4 ft/s

Note that in the equation is v^2=-u^2 + 2gh the mass of the object has no place. So, The final velocity is independent of the mass

so the final velocity of the 100 pound ball will also be 25.4 ft/s

Now let us find the time taken for the 1 pound ball

v = u + gt\\\\25.4 = 0+ 32.2t\\\\t = 0.788s

Since the equation v = u + gt does not depend on mass, the 100 pound ball will also reach the ground at time t = 0.788 s

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Consider an elevator with a table and a book on top of the table. The mass of the table is 10kg and the mass of the book is 2kg.
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Newton's second law allows us to find the force of the block on the table is 126 N

Newton's second law says that the net force is proportional to the product of the mass and the acceleration of the body

                Σ F = m a

Where the bold letters indicate vectors, m is the mass and the acceleration of the body

A free body diagram is a diagram where the forces are represented without the details of the bodies, in the attached we can see a free body diagram of the system.

Let's start by finding the acceleration of the elevator with kinematics  

                 v = v₀ + a t

                 a = \frac{v-v_o}{a}  

Where v and v₀ are the current and initial velocity, respectively, at acceleration and t is the time

                 a = \frac{8-1}{2}

                 a = 3.5 m / s²

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The book

                N₂ - W₂ + N₁ = m a

               

Table

                N₁ - W₁ - W₂ = M a

                W₁ = Mg

                W₂ = mg

                N₁ = (M + m) g + M a

                N₁ = (10 + 2) 9.8 + 10 3.5

                N₁ = 152.6 N

This is the reaction of the earth to the support of the block and the table

               N₂ = ma + m g  - N₁

               N₂ = m ( a +g) - N₁  

               N₂ = 2 (3.5 + 9.8) - 152.6

               N₂ = 26.6 - 152.6

               N₂ = -126 N

The negative sign indicates that the direction is opposite to the one assigned, this is the action of the block on the table.

In conclusion using Newton's second law we can find the forces of the block on the table is 126 N

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