A group of construction workers are building a house and want to lower an excess bundle of bricks that has a mass of 249 kg from the second story window to the ground. They tie one end of a rope to the bundle of bricks, loop it through a pulley and tie the other end to a 124.5 kg toolbox. If the coefficient of kinetic friction between the toolbox and the floor is 0.410, what is the acceleration of the bundle of bricks? 9.80 m/s2 0.530 m/s2 5.19 m/s2 15.6 m/s2
Question
A group of construction workers are building a house and want to lower an excess bundle of bricks that has a mass of 249 kg from the second story window to the ground. They tie one end of a rope to the bundle of bricks, loop it through a pulley and tie the other end to a 124.5 kg toolbox. If the coefficient of kinetic friction between the toolbox and the floor is 0.410, what is the acceleration of the bundle of bricks? 9.80 m/s2 0.530 m/s2 5.19 m/s2 15.6 m/s2
Solution
To solve this problem, we need to use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
First, let's calculate the force of gravity on the bundle of bricks and the toolbox.
The force of gravity (Fg) is equal to the mass (m) of an object times the acceleration due to gravity (g), which is approximately 9.8 m/s^2 on Earth.
So, the force of gravity on the bundle of bricks is:
Fg_bricks = m_bricks * g = 249 kg * 9.8 m/s^2 = 2440.2 N
And the force of gravity on the toolbox is:
Fg_toolbox = m_toolbox * g = 124.5 kg * 9.8 m/s^2 = 1220.1 N
Next, let's calculate the force of friction (Ff) acting on the toolbox. The force of friction is equal to the coefficient of friction (μ) times the normal force (Fn). In this case, the normal force is equal to the force of gravity on the toolbox, so:
Ff = μ * Fn = 0.410 * 1220.1 N = 500.241 N
Now, we can calculate the net force (Fnet) acting on the system. The net force is equal to the force of gravity on the bricks minus the force of gravity on the toolbox and the force of friction:
Fnet = Fg_bricks - Fg_toolbox - Ff = 2440.2 N - 1220.1 N - 500.241 N = 719.859 N
Finally, we can calculate the acceleration (a) of the bundle of bricks. The acceleration is equal to the net force divided by the mass of the bricks:
a = Fnet / m_bricks = 719.859 N / 249 kg = 2.89 m/s^2
So, the acceleration of the bundle of bricks is approximately 2.89 m/s^2. This option is not listed in the given choices, so there might be a mistake in the problem or in the calculations.
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