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Katena32 [7]
3 years ago
12

What must be the reaction force when someone hits a tree with an axe?

Physics
1 answer:
Iteru [2.4K]3 years ago
7 0

Answer: The correct option is that the axe handle applying a force to the person's hand.

Explanation:

This reaction force is due to Newton's third law of motion. This law states that for every action there is equal and opposite reaction to it. This implies that when a force is being exerted on a surface, the surface must exert a force that is equal and opposite in direction to the exerting force. This law represents a certain symmetry in nature that forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself.

A typical example of Newton's third law includes:

--> When you hit a tree with an axe: with your hand you exert a force on the tree with the intention to cut it down(action force). The same force you excreted on the tree would be felt in your hands (reaction force).

--> when air rushes out of a balloon: when air escapes for a balloon, the opposite reaction is that the balloon flies up.

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1) 5.5 N

When the ball is at the bottom of the circle, the equation of the forces is the following:

T-mg = m\frac{v^2}{R}

where

T is the tension in the string, which points upward

mg is the weight of the string, which points downward, with

m = 0.158 kg being the mass of the ball

g = 9.8 m/s^2 being the acceleration due to gravity

m \frac{v^2}{R} is the centripetal force, which points upward, with

v = 5.22 m/s being the speed of the ball

R = 1.1 m being the radius of the circular trajectory

Substituting numbers and re-arranging the formula, we find T:

T=mg+m\frac{v^2}{R}=(0.158 kg)(9.8 m/s^2)+(0.158 kg)\frac{(5.22 m/s)^2}{1.1 m}=5.5 N

2) 3.9 N

When the ball is at the side of the circle, the only force acting along the centripetal direction is the tension in the string, therefore the equation of the forces becomes:

T=m\frac{v^2}{R}

And by substituting the numerical values, we find

T=(0.158 kg)\frac{(5.22 m/s)^2}{1.1 m}=3.9 N

3) 2.3 N

When the ball is at the top of the circle, both the tension and the weight of the ball point downward, in the same direction of the centripetal force. Therefore, the equation of the force is

T+mg=m\frac{v^2}{R}

And substituting the numerical values and re-arranging it, we find

T=m\frac{v^2}{R}-mg=(0.158 kg)\frac{5.22 m/s)^2}{1.1 m}-(0.158 kg)(9.8 m/s^2)=2.3 N

4) 3.3 m/s

The minimum velocity for the ball to keep the circular motion occurs when the centripetal force is equal to the weight of the ball, and the tension in the string is zero; therefore:

T=0\\mg = m\frac{v^2}{R}

and re-arranging the equation, we find

v=\sqrt{gR}=\sqrt{(9.8 m/s^2)(1.1 m)}=3.3 m/s

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Explanation:

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Why is it important that two different metals are used in building an electrochemic<br> cell?
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