Kinematics
A ball is thrown straight upward from the edge of a building. A student says, "At the highest point, both velocity and acceleration are zero." Identify exactly which part of the statement is wrong and explain what the ball does immediately afterward.
The vertical velocity is zero at the highest point, but the acceleration is still downward at g. Immediately afterward, the ball begins moving downward because it continues to accelerate downward.
A block is sliding upward along a rough incline. Give the direction of gravity, the normal force, and friction.
Gravity points vertically downward. The normal force points perpendicular to and away from the incline. Friction points down the incline because it opposes the block's upward motion.
A horizontal force on a box increases from 0 N to 20 N, but the box remains at rest. What happens to the static friction force as the applied force increases?
Static friction increases to match the applied force as needed, as long as the maximum static friction has not been reached.
A car travels around a circular track at constant speed. Which of the following is constant: velocity, acceleration vector, speed, or net force vector?
Speed is constant. Velocity changes because its direction changes. The acceleration vector and net force vector also change direction as the car moves around the circle.
A person walks forward at 2 m/s relative to a train that is moving forward at 15 m/s relative to the ground. What is the person's velocity relative to the ground?
17 m/s forward.
Two balls start at the same height at the same instant. Ball A is dropped straight down. Ball B is launched horizontally at 20 m/s. Ignoring air resistance, which ball has the greater vertical velocity immediately before hitting the ground, and which has the greater total speed?
They have the same vertical velocity immediately before hitting the ground. Ball B has the greater total speed because it also has a horizontal velocity component.
A box is pulled to the right across a horizontal floor using a rope angled upward. Compared with pulling horizontally using the same tension magnitude, does the normal force increase, decrease, or stay the same? Explain why.
The normal force decreases. The upward component of the tension helps support the weight of the box, so the floor does not need to provide as much upward normal force.
A block is motionless on an incline. A student automatically uses fs = musN. What assumption has the student made?
The student has assumed that the block is exactly at the threshold of slipping, meaning static friction has reached its maximum value.
An object moves clockwise around a circle. At one instant it is at the leftmost point of the circle. What direction is its velocity? What direction is its centripetal acceleration?
Its velocity points upward. Its centripetal acceleration points to the right, toward the center of the circle.
A person pushes a heavy box, but the box does not accelerate. Is the box exerting a force back on the person? Is that force the reason the net force on the box is zero?
Yes, the box pushes back on the person. No, that reaction force is not part of the force balance on the box because it acts on the person, not on the box.
A projectile is launched at an angle. At one point in its motion, its velocity is 16 m/s horizontally and 0 m/s vertically. Without solving for time, identify where the projectile is in its path, the direction of its acceleration, and whether its speed will increase or decrease immediately afterward.
It is at the top of its trajectory. Its acceleration points downward. Immediately afterward, its speed begins increasing because its downward vertical velocity starts increasing while its horizontal velocity remains constant.
Two blocks hang on opposite sides of an ideal pulley. Block 2 is heavier than Block 1. For Block 1 only, state the direction of acceleration, whether tension is greater than, less than, or equal to its weight, and write the force equation if upward is positive. (DAILY DOUBLE)
Block 1 accelerates upward. Tension is greater than its weight. The equation is T - m1g = m1a.
A bottom block is accelerated to the right. A smaller block sits on top and does not slip. What force causes the top block to accelerate to the right? What direction is the friction force exerted by the top block on the bottom block?
Static friction from the bottom block causes the top block to accelerate to the right. By Newton's Third Law, the top block exerts a friction force on the bottom block to the left.
A car drives around a flat circular road. What actual force can provide the inward acceleration? Why should "centripetal force" not be drawn as an additional force on the free-body diagram?
Static friction between the tires and the road can provide the inward force. Centripetal force is not a new force. It is the name for the net force directed toward the center.
A boat travels north at 8 m/s relative to the water while the water itself moves east at 6 m/s. What is the boat’s speed relative to someone standing on the shore, and in what direction does the boat actually move?
The boat’s speed relative to shore is 10 m/s. It moves northeast because its northward motion combines with the eastward motion of the water.
A projectile lands at the same vertical height from which it was launched. At two different times, one on the way up and one on the way down, it is at the same vertical position. Compare its horizontal velocity, magnitude of vertical velocity, direction of vertical velocity, and acceleration at those two points.
The horizontal velocity is the same. The magnitude of the vertical velocity is the same. The vertical velocities point in opposite directions. The acceleration is the same at both points and points downward.
A block rests motionless on an incline. A student draws four forces on the free-body diagram: normal force perpendicular to the incline, friction up the incline, mgsin(theta) perpendicular to the incline, and mgcos(theta) down the incline. What is wrong with the diagram?
mgsin(theta) should be down the incline and mgcos(theta) should be perpendicular to the incline.
A box of mass m is pulled horizontally with force F and does not move. You are told that musmg is greater than F. What is the actual magnitude of the static friction force? Why is it not equal to musmg?
The static friction force is equal to F. musmg gives the maximum possible static friction, not the actual static friction unless the box is exactly at the point of slipping.
Two identical cars travel around the same circular track. Car A travels at speed v. Car B travels at speed 2v. Compare the required inward net forces.
Car B requires four times the inward force of Car A because centripetal acceleration depends on v squared.
A boat moves north at 6 m/s relative to the water while the water moves east at 8 m/s. If the boat turns around and moves south at 6 m/s relative to the water, does its speed relative to shore change?
No. Its speed relative to shore is 10 m/s in both cases. Only the direction changes.
A projectile is launched from the ground with an initial horizontal velocity of 12 m/s and an initial vertical velocity of 16 m/s. Use g = 10 m/s^2. A student says that after 1.6 seconds, the projectile has stopped moving because its vertical velocity is zero. Give two reasons why this conclusion is wrong.
Its vertical velocity is zero, but its horizontal velocity is still 12 m/s. Its acceleration is still downward. It is only at the highest point of its path and continues moving horizontally while beginning to accelerate downward.
You are given a two-block system connected by a rope over a pulley, but the problem does not tell you which direction the system will move.
What should you do before writing your final force equations?
Choose a direction of motion and define it as positive. Draw the free-body diagrams based on that assumed motion, including friction opposing the assumed motion. Then write the force equations using that sign convention.
If the acceleration comes out positive, your assumed direction was correct.
If the acceleration comes out negative, the system actually moves in the opposite direction.
(DAILY DOUBLE) A block starts at rest on a rough horizontal floor. You slowly increase the applied force until the block begins moving. After it starts moving, you adjust the force until the block travels at a constant speed.
How must the applied force have changed during this process?
At first, the applied force had to increase until it exceeded the maximum static friction, approximately μsN. Once the block started moving, friction changed to kinetic friction. Since μs is greater than μk, the applied force then had to decrease. For the block to move at constant speed, the applied force must eventually equal the kinetic friction force, approximately μkN.
A car travels around a circular path at constant speed. At one instant, its velocity points east. A student says, "The net force must also point east because F = ma and the car is moving east." Explain why this is wrong and identify the possible directions the net force points toward the center of the circle.
Force points in the direction of acceleration, not velocity. In circular motion, the acceleration is perpendicular to the velocity and points toward the center. If the velocity points east, the center must be either north or south of the car, depending on which way the car is turning.
Two blocks are touching on a frictionless floor. You push Block A to the right, and both blocks accelerate together. Block B has twice the mass of Block A.
Which is greater: the force of A on B, or the force of B on A? Then explain why Block B can still have a different acceleration if the interaction forces are equal.
The force of A on B and the force of B on A are equal in magnitude because of Newton’s Third Law.
If the blocks are accelerating together, they actually have the same acceleration. The difference is that the forces acting on each block are not the same overall. Newton’s Third Law only says the interaction pair between A and B is equal and opposite; it does not mean the net force on each block is the same (They are different because one block has Fpush while another doesn't).