Physics 1: Free Body Diagrams

A M##_1## = 5 kg box rests on a table and is connected to a second box of mass M##_2## = 10 kg via a rope that hangs over a frictionless pulley as shown. The coefficient of friction, ##\mu## is 0.2, Use free body diagrams to answer the following:
B. What is the tension in the rope?

A M##_1## = 6 kg box rests on a table and is connected to a second box of mass M##_2## = 5 kg via a rope that hangs over a frictionless pulley as shown. The coefficient of friction, ##\mu## is 0.15, Use free body diagrams to answer the following:
B. What is the tension in the rope?

A M##_1## = 8 kg box rests on a table and is connected to a second box of mass M##_2## = 4 kg via a rope that hangs over a pulley as shown. The coefficient of static friction, ##\mu_s## is 0.2, and the coefficient of kinetic friction ##\mu_k## is 0.1. Use a free body diagrams to answer the following.
B. If the box does cause the system to move, what is the acceleration of the system, and the tension in the rope?

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.)

The large block m##_1## is 10 kg, and the smaller block m##_2## is 1 kg. The coefficient of kinetic friction is 0.1. Determine the acceleration of the system and the contact force between the blocks. The applied force, F is 30 N. Also draw a free body diagram for both blocks.

The large block m##_1## is 6 kg, and the smaller block m##_2## is 12 kg. The coefficient of kinetic friction is 0.2. Determine the acceleration of the system and the Tension T##_2## . The applied force, F is 36 N. Also draw a free body diagram for both blocks.

A ball of mass ##M## is thrown vertically upward with an initial speed of ##v_0##. It experiences a force of air resistance given by ##F = -kv##, where ##k## is a positive constant. The positive direction for all vector quantities is upward. Express all algebraic answers in terms of ##M##, ##k##, ##v_0##, and fundamental constants.

• Does the magnitude of the acceleration of the ball increase, decrease, or remain the same as the ball moves upward?
• Write, but do NOT solve, a differential equation for the instantaneous speed ##v## of the ball in terms of time ##t## as the ball moves upward.
• Determine the terminal speed of the ball as it moves downward.
• Does it take longer for the ball to rise to its maximum height or to fall from its maximal height back to the height from which it was thrown? Justify your answer.
• Sketch a graph of velocity versus time for the upward and downward parts of the ball's flight, where ##t_f## is the time at which the ball returns to the height from which it was thrown.

A small block of mass ##M_B## = 0.50 kg is placed on a long slab of mass ##M_S## = 3.0 kg as shown below. Initially, the slab is at rest and the block has a speed ##v_0## of 4.0 m/s to the right. The coefficient of kinetic friction between the block and slab is 0.20, and there is no friction between the slab and the horizontal surface on which it moves.

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.

• 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 ##v## of the ball in terms of time ##t## , the given quantities, and fundamental constants.
• Determine the terminal speed ##v_t## in 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 ##h## and 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)

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