Two packing crates of masses m_{1} = 5.00 kg and m_{2} = 13.0 kg are connected by a light string that passes over a trictionless pulley as in the Figure. The 12.0 kg crate lies on an incline of angle 40.0^ , . The coefficient of friction between my and the incline is 0.150.
Determine the normal force of m2. Round to 3sig fig
Determine the force of friction on m2. Round to 3 dig fig
Determine the tension in the string
To determine the normal force on m2, we need to consider the forces acting on it. In this case, the normal force is the force exerted by the incline on the crate perpendicular to the incline.
Here's how you can find the normal force on m2:
1. Draw a free-body diagram for m2. This will help us visualize the forces acting on it.
* There is the weight acting vertically downward (mg), where g is the acceleration due to gravity.
* There is the tension in the string acting upward.
* There is the normal force, perpendicular to the incline, acting upward.
* There is the force of friction acting parallel to the incline, opposing the motion.
2. Resolve the force of gravity into components.
The weight of m2 can be divided into two components:
* The component perpendicular to the incline is mg * cos(40°).
* The component parallel to the incline is mg * sin(40°).
3. Recognize that the normal force is equal in magnitude but opposite in direction to the perpendicular component of the weight.
Therefore, the normal force on m2 is mg * cos(40°).
4. Substitute the given values into the equation.
m2 = 13.0 kg
g = 9.8 m/s²
θ = 40°
normal force = 13.0 kg * 9.8 m/s² * cos(40°)
Calculate the result, rounding to three significant figures.
To determine the force of friction on m2, we need to consider the coefficient of friction and the normal force acting on it. The force of friction can be calculated using the equation:
force of friction = coefficient of friction * normal force
Substitute the given values, including the normal force we calculated earlier, into the equation. Round the result to three significant figures.
Finally, to determine the tension in the string, we need to consider the forces acting on m1. The tension in the string is equal to the force required to overcome the force of friction acting on m2. Therefore, the tension in the string is equal to the force of friction on m2.
Substitute the force of friction we calculated earlier into the equation to find the tension in the string. Round the result to three significant figures.