# Physics Homework Help

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 bv2, where bis a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient bis 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.

Draw and label all the forces on the ball at some instant before it reaches terminal speed.

State whether the magnitude of the acceleration of the ball of mass m increases, decreases, or remains the same as the ball approaches terminal speed. Explain.

Write, but do NOT solve, a differential equation for the instantaneous speed vof the ball in terms of time t, the given quantities, and fundamental constants.

Determine the terminal speed vtin terms of the given quantities and fundamental constants.

Determine the energy dissipated by the drag force during the fall if the ball is released at height hand reaches its terminal speed before hitting the ground, in terms of the given quantities and fundamental constants. (this question requires knowledge of potential and kinetic energy, often not introduced until later in a physics course)

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## Related Problems

As shown in the figure, two blocks with masses m and M (M>m) are pushed by a force F in both Case I and Case II. The surface is horizontal and frictionless. Let R1 be the force that m exerts on M in Case I and RII be the force that m exerts on M in Case II. Which of the following statements is true?

Two boxes with masses 17 kg and 15 kg are connected by a light string that passes over a frictionless pulley of negligible mass as shown in the figure below. The surfaces of the planes are frictionless. The blocks are released from rest. T1 and T2 are the tensions in the strings. Which of the following statements is correct?

An Object with mass m and initial velocity v is brought to rest by a constant force F acting for a time t and through a distance d. Possible expressions for the magnitude of the force F are: i. $\frac{mv^2}{2d}$ ii. $\frac{2md}{t^2}$ iii. $\frac{mv}{t}$

ii only

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A toy car of mass 6 kg moving in a straight path, experiences a net force given by the function F = -3t. At time t=0, the car has a velocity of 4 m/s in the positive direction and is located +8 m from the origin. The car will come instantaneously to rest at time t equal to

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sqrt( 4/3 ) s

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4 s