A group of construction workers are building a house and want to lower down an excess bundle of 2380 kg bricks to ground. They tie one end of a rope to the bundle of bricks, loop it through a pulley, and tie the other end of the rope to a toolbox. If the coefficient of kinetic friction between the toolbox and the floor is 0.650 and the acceleration of the bundle of bricks is 5.71 m/s2, what is the mass of the toolbox? 1.47×104 kg 2.81×103 kg 806 kg 1.76×103 kg
Question
A group of construction workers are building a house and want to lower down an excess bundle of 2380 kg bricks to ground. They tie one end of a rope to the bundle of bricks, loop it through a pulley, and tie the other end of the rope to a toolbox. If the coefficient of kinetic friction between the toolbox and the floor is 0.650 and the acceleration of the bundle of bricks is 5.71 m/s2, what is the mass of the toolbox? 1.47×104 kg 2.81×103 kg 806 kg 1.76×103 kg
Solution
To solve this problem, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma).
The force acting on the toolbox is the weight of the bricks (which is their mass times the acceleration due to gravity) minus the force of friction (which is the coefficient of kinetic friction times the normal force).
The normal force in this case is the weight of the toolbox (its mass times the acceleration due to gravity).
So, we can set up the following equation:
F = ma m_brickg - μm_toolboxg = m_toolboxa
where: m_brick is the mass of the bricks (2380 kg), g is the acceleration due to gravity (9.8 m/s²), μ is the coefficient of kinetic friction (0.650), m_toolbox is the mass of the toolbox (which we're trying to find), and a is the acceleration of the bricks (5.71 m/s²).
We can rearrange this equation to solve for m_toolbox:
m_toolbox = (m_brickg - μm_toolbox*g) / a
This is a linear equation in m_toolbox, which we can solve by isolating m_toolbox on one side of the equation:
m_toolbox = (m_brickg) / (a + μg)
Substituting the given values into this equation gives:
m_toolbox = (2380 kg * 9.8 m/s²) / (5.71 m/s² + 0.650 * 9.8 m/s²)
Solving this equation gives the mass of the toolbox, which is approximately 2.81×10³ kg. So, the correct answer is 2.81×10³ kg.
Similar Questions
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