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A box is being pulled with force F\(_a\) = 40 N at an angle \(\theta\) = 30 degrees. There is a frictional force opposing the sliding of the box with force F\(_f\) = 10 N. Draw a free body diagram to help answer the following questions. (use gravity at 10m/s\(^2\) to simplify the numbers)
A 5 kg lawn mower is being pushed with an applied force of F\(_a\) = 20 N, at an angle of \(\theta\) . There is a frictional force, F\(_f\) opposing the movement of the lawn mower of 10 N. Given that the lawn mower is accelerating at 0.4 m/s\(^2\):
A block of mass \(m\) is pulled along a rough horizontal surface by a constant applied force of magnitude \(F_1\) that acts at an angle \(\theta\) to the horizontal, as indicated below. The acceleration of the block is \(a_1\) . Express all algebraic answers in terms of \(m\) , \(F_1\) , \(\theta\) , \(a_1\) , and fundamental constants.
A rubber ball of mass \(m\) is dropped from a cliff. As the ball falls, it is subject to air drag (a resistive force caused by the air). The drag force on the ball has a magnitude \(bv^2\) , where \(b\) is a constant drag coefficient and \(v\) is the instantaneous speed of the ball. The drag coefficient \(b\) is directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.
A student is swinging a mass, m = 2.0 kg, in a uniform vertical circle of radius R = 2.5 m. The period of the rotation is 2.8 seconds. Draw a free body diagram for the mass at the top of the circle and find the tension of the string (ignore friction and the mass of the string.) Repeat for the mass at the bottom of the rotation.