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Answer :
your answer is m = 59 kg
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Rewritten by : Barada
The most massive trunk you will be able to move is approximately [tex]\( 69.2 \, \text{kg} \)[/tex]. So, the closest option is 67 kg.
To find the maximum mass of the trunk you can move, we need to consider the maximum force of static friction that can be exerted by the floor on the trunk. The maximum force of static friction[tex](\( F_{\text{friction}} \))[/tex] can be calculated using the formula:
[tex]\[ F_{\text{friction}} = \mu_s \times N \][/tex]
Where:
-[tex]\( \mu_s \)[/tex] is the coefficient of static friction,
- [tex]\( N \)[/tex] is the normal force exerted by the floor on the trunk.
The normal force[tex](\( N \))[/tex] can be calculated as the vertical component of the force you exert on the trunk:
[tex]\[ N = F_{\text{vertical}} = F \times \cos(\theta) \][/tex]
Where:
- F is the force you exert on the trunk (750 N in this case),
- [tex]\( \theta \)\\[/tex] is the angle of the force with the horizontal (25° in this case).
Substituting the given values:
[tex]\[ N = 750 \, \text{N} \times \cos(25^\circ) \]\[ N \approx 750 \, \text{N} \times 0.906 \]\[ N \approx 679.5 \, \text{N} \][/tex]
Now, we can calculate the maximum mass m of the trunk using the formula:
[tex]\[ F_{\text{friction}} = m \times g \][/tex]
Where:
- m is the mass of the trunk,
- g is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)).[/tex]
Substituting the given values:
[tex]\[ 679.5 \, \text{N} = m \times 9.81 \, \text{m/s}^2 \]\[ m = \frac{679.5 \, \text{N}}{9.81 \, \text{m/s}^2} \]\[ m \approx 69.2 \, \text{kg} \][/tex]
Therefore, the most massive trunk you will be able to move is approximately [tex]\( 69.2 \, \text{kg} \)[/tex]. So, the closest option is 67 kg.
