# Physics 1

A Jogger runs with constant speed $v$ through a forest of pine trees. A pine cone starts to fall from a height $h$ when the jogger is directly below it. How far behind the jogger will the pine cone land?

In a rescue attempt, a hovering helicopter drops a life preserver to a swimmer being swept downstream by a river current of a constant velocity v. The helicopter is at a height of 9.8 m. The swimmer is 6.0 m upstream from a point directly under the helicopter when the life preserver is released. It lands 2.0 m in front of the swimmer. How fast is the current flowing? Neglect air resistance.

13.7 m/s

9.8 m/s

6.3 m/s

2.8 m/s

A child tosses a ball directly upward. Its total time in the air is T. Its maximum height is H. What is its height after it has been in the air at time T/4? Neglect air resistance.

H/4

H/3

H/2

2H/3

3H/4

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach as shown in the figure. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity? (c) Write the equations for the x- and y-components of the velocity of the stone with time. (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (e) How long after being released does the stone strike the beach below the cliff? (f) With what speed and angle of impact does the stone land?

A block of mass M1 on a horizontal table is connected to a hanging block of mass M2 by a string that passes over a pulley, as shown in the figure below. The acceleration of the blocks is 0.6g. Assume that friction and the mass of the string are negligible. The tension T in the string is

A block of mass M = 5kg is placed on an incline of $\theta$ = 30 degrees. There is a frictional force opposing the movement of the block with a coefficient of friction, $\mu$ = 0.2. Determine the acceleration of the block. Draw a free body diagram to help find the answer.

Determine the acceleration of the system if M = 10 kg and m = 30 kg and $\theta$ = 30 degrees. Determine the tension in the rope as well.

Block M = 5 kg and block m = 3 kg. The coefficient of static friction is 0.2. Determine the acceleration of the system and the tension in the cord. The angle of the inclined plane is 30 degrees to the horizontal. Draw a free body diagram for the 5 kg block to help find the answer.

The large block m$_1$ is 10 kg, and the smaller block m$_2$ is 5 kg. The applied force, F is 100 N. The large block m$_1$ experiences a 40 N frictional force opposing the applied force, and the smaller block m$_2$ experiences a 20 N frictional force. Find the action-reaction force between the boxes. (This question requires Newton's Third Law.)

What is the tension T in the rope if the 10-N weight is moving upward with a constant velocity?

A car of mass 100 kg is traveling in a circle of radius 20 m. There is a frictional force of 500 N on the car's wheels (in the direction of the center of the circle, to keep the car going in a circle). Draw a free body diagram for the car and find the velocity of the car.

The 100 kg box shown below is being pulled along the x-axis by a student. The box slides across a rough surface, and its position $x$ varies with time $t$ according to the equation $x = 0.5t^3 + 2t$ , where $x$ is in meters and $t$ is in seconds.

C. Calculate the net work done on the box in the interval $t$ = 0 to $t$ = 2 s would be greater than, less than, or equal to the answer in part (C). Justify your answer.

The figure below depicts a roller coaster. Assume the roller coaster starts at a velocity of 0 m/s from 70 m.

B. Determine the height of the track at point x. It is known that the roller coaster has a velocity of 30 m/s at x.

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

B. 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.

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

D. Determine the terminal speed $v_t$ in terms of the given quantities and fundamental constants.

E. Determine the energy dissipated by the drag force during the fall if the ball is released at height $h$ and reaches its terminal speed before hitting the ground, in terms of the given quantities and fundamental constants.

In the system of two blocks and a spring shown below, blocks 1 and 2 are connected by a string that passes over a pulley. The initially unstretched spring connects block 1 to a ridged wall. Block 1 is released from rest, initially slides to the right, and is eventually brought to rest by the spring and the friction on the horizontal surface. Which of the following is true of the energy of the system during the process?

E. The potential energy lost by block 2 is greater in magnitude than the potential energy gained by the spring

A rope of length $L$ is attached to a support at point C. A person of mass $m_1$ sits on a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown below. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass $m_2$ is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and object then land together in the lake at point D, which is a vertical distance $L$ below position B. Air resistance and the mass of the rope are negligible. Derive expression for each of the following in terms of $m_1$ , $m_2$ , $L$ , and $g$.

E. The total horizontal displacement x of the person from position A until the person and object land in the water at point D.

A 50 kg object is to be launched 7 x 10$^6$ m out into space (not into orbit, it will fall back to earth). Given that the radius of the earth is 6.4 x 10 $^6$ m and the mass of the earth is 6.0 x 10 $^{24}$ kg, find:

A. The work done to put the object that far into space.

B. The total kinetic energy of the object required to put the object that far into space.

C. The binding energy.

D. The escape velocity.

A 60 kg object is to be launched into orbit, 7 x 10$^6$ m above the Earth's surface. Given that the radius of the earth is 6.4 x 10 $^6$ m and the mass of the earth is 6.0 x 10 $^{24}$ kg, find:

A. The work done to put the object into orbit.

B. The velocity required to put the object into orbit.

C. The velocity of the object once it is in orbit.