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An aluminum block, m1 = 3.00 kg, and a copper block, m2 = 1.14 kg, are connected by a light string over a frictionless pulley. They sit on a steel surface as shown in the figure below, where θ = 45.0°. (See the table below for the appropriate coefficients of friction).
Determine the sum of the magnitudes of the forces of friction acting on the blocks.
Where is the table?
To determine the sum of the magnitudes of the forces of friction acting on the blocks, we need to consider the coefficients of friction given in the table and the forces acting on each block.
Here are the steps to find the sum of the magnitudes of the forces of friction:
1. Identify the forces acting on each block:
- For the aluminum block (m1), the forces acting are its weight (mg1) and the force of friction ("fa").
- For the copper block (m2), the forces acting are its weight (mg2) and the force of friction ("fc").
2. Calculate the weight of each block:
- The weight of the aluminum block (m1) is given by: mg1 = m1 * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
- The weight of the copper block (m2) is given by: mg2 = m2 * g.
3. Determine the force of friction for each block:
- For the aluminum block (m1), the force of friction (fa) can be calculated using the equation: fa = μa * N1, where μa is the coefficient of friction between the aluminum block and the steel surface, and N1 is the normal force acting on the block. The normal force (N1) can be found using the equation: N1 = mg1 * cos(θ), where θ is the angle of inclination (45.0°).
- For the copper block (m2), the force of friction (fc) can be calculated using the equation: fc = μc * N2, where μc is the coefficient of friction between the copper block and the steel surface, and N2 is the normal force acting on the block. The normal force (N2) can be found using the equation: N2 = mg2 * cos(θ).
4. Calculate the sum of the magnitudes of the forces of friction:
- The sum of the magnitudes of the forces of friction can be found by adding the magnitudes of the individual forces of friction: sum = |fa| + |fc|.
Make sure to refer to the given table for the appropriate coefficients of friction between the blocks and the steel surface.
Note: If the direction of the forces of friction is not specified in the question, we assume they act in opposite directions to the motion of the blocks.