MCAT Physics Ch. 1: Kinematics and Dynamics

Describe Newton's Three Laws

1. First Law: F = ma A body at rest will stay at rest, while a body in motion will stay in motion unless some external force is acting on it. [also known as the law of inertia] 2. second law: an object will accelerate when the net force imposed on it is non-zero 3. Third Law: for every action, there is an equal and opposite reaction

Multiplying vectors: 1. A * B (dot product) 2. A x B (cross-product)

1. |A||B|cos(theta) 2. |A||B|sin (theta)

A Boeing 747 aircraft has a landing speed of 72 m/s, and upon landing it is able to come to a stop in 2,000 m. Assuming constant deceleration, how long would it take for a Boeing 747 to come to a full stop?

56 sec

Question

Aisha is pulling with 20N, so in order for this system to be in equilibrium, Saul and Lorenzo together must be pulling with the same force in the opposite direction. That vector would represent the hypotenuse of the right triangle where Saul's force is the adjacent side and Lorenzo's opposite. Hint #2 One big clue to solving this problem is that the angle is equal to arctan(1.33). 1.33 is the value of the opposite side divided by the adjacent side. Hint #3 Let's represent the decimal by a fraction, which would be 4/3. So the ratio of the opposite side to the adjacent side is 4:3. Hint #4 Either by Pythagorean theorem or by past memorization, the hypotenuse will have the value of 5, and we have our 3-4-5 triangle. Hint #5 As we said, Aisha represents the hypotenuse, which has a value of 20N. Divide that by the calculated value for the hypotenuse to obtain the factor to multiply the other sides. That factor is 4. Hint #6 The other sides of the triangle are 12 N and 16 N. Match it to the right person. The correct answer is 16 N for Lorenzo and 12 N for Saul.

An object is dropped from the top of the Empire State Building. Which of the following statements best describes the motion of the object as it experiences air resistance during its downward fall? A.The speed will decrease at a constant rate for its fall. B.Its acceleration will decrease until the object starts moving with a constant speed. C.Its speed remains constant for the fall. D.The speed will increase at a constant rate for its fall.

Answer: B The force of air resistance is proportional to the square of the velocity. At the beginning, there is no upward force. As the object falls through the sky, the force of air resistance increases and increases to oppose the force due to gravity. Hint #2 As time progresses further, the force of air resistance will increase until it is equal in magnitude and opposite in direction to the weight. Hint #3 Its speed does not remain constant for the fall and does not decrease at a constant rate since it gain more speed as it falls. Hint #4 The speed does increase, but not at a constant rate and not for the entirety of its fall.

Which of the following statements correctly identifies an example of the respective scalar or vector product processes? I. Vector and scalar : torque II. Vector and vector : magnetic force III. Scalar and scalar : power Please choose from one of the following options. III only I and II I only II and III

Answer: II and III A scalar multiplied by a scalar will produce another scalar. For instance, distance divided by time is equal to speed, which is a scalar. In the case of power, energy divided by time is equal to power. Statement III is true. Hint #2 A vector multiplied by a scalar is representative of the scalar product or the dot product and will always produce a vector. The scalar product of two vectors A and B can be constructed by taking the component of A in the direction of B and multiplying it times the magnitude of B, and it can be expressed as ABcosθ. Hint #3 Torque is not an example of the scalar product of vectors since it is equal to rFsinθ. A correct example of the dot product would be work, which is equal to Fdcosθ. Therefore, statement I is not true. Hint #4 Vector multiplied by a vector is representative of the vector product or the cross product and will produce a vector or scalar. The magnitude of the vector product of A and B can be constructed by taking the product of the magnitudes of A and B multiplied by the sine of the angle between them. Hint #5 Magnetic force is an example of the vector cross product, so statement II is true. Therefore, the correct answer is that statements II and III are true.

A block of mass m is sliding at a positive constant acceleration down the a plane with an incline of θ, a coefficient of static friction of μ_s and a coefficient of kinetic friction μ_k Which of the following expressions represents the net force on the block? A.mg cos θ - μ_k mg sin θ B.mg sin θ - μ_s mg cos θ C.mg sin θ - μ_kmg cos θ D.mg cos θ - μ_smg sin θ

C

Equation for calculating centripetal force

F = (mv^2)/r centripetal force can be caused by tension, gravity, electrostatic force, or other forces

A block of mass m is sitting motionless on a plane with an incline of θ, a coefficient of static friction of μ_s, and a coefficient of kinetic friction μ_k Which of the following will occur once the plane is elevated on one side, increasing θ? A.The maximum force caused by static friction will increase. B.The maximum force caused by static friction will decrease. C.The coefficient of static friction μ_s will decrease. D.The coefficient of kinetic friction μ_k will decrease.

The coefficients of friction, both kinetic and static, are not affected by the slope angle of the surface and stays constant throughout the elevation. The coefficient of friction is determined experimentally and is usually only affected by the types of materials used in the interface between the surfaces of the object and plane. Hint #2 The maximum force of static friction is proportional to the normal force. Hint #3 The normal force is decreased as the plane is elevated because the component of gravitational force directed into the plane (F_g ​g Increases. Therefore, as θ increases, the maximum force caused by static friction will decrease.

Incline Questions

The only forces on the object include the gravitational force, and the normal force. Hint #2 Since the normal force is acting perpendicular to the acceleration down the incline plane, we do not need to consider its contribution in our determination of the acceleration. Hint #3 The gravitational force is not directly parallel to the plane's slope, thus necessitating that the gravitational force split into its two perpendicular components.

An ambulance is currently traveling at 15m/s, and is accelerating with a constant acceleration of 5 m/s^2.The ambulance is attempting to pass a car which is moving at a constant velocity of 30m/s. How far must the ambulance travel until it matches the car's velocity?. A.67.5 m B.45 m C.90 m D.67.5 km

a

Torque Question

f the force acts downwards to the left or upwards to the right of the fulcrum, then there is a counterclockwise (CCW) torque. If the force acts downwards to the right or upwards to the left of the fulcrum, then there is a clockwise (CW) torque. Hint #2 Forces will act from the center of mass if possible, and the fulcrums are the top right edge of Block 2 and the left edge of the desk. Hint #3 If Block 2 were shifted to the left, the center of mass moves to the left of the fulcrum, so the weight creates a CCW torque, not CW. The weight of Block 1 acts to the right of the same fulcrum downwards creating a CW torque, not CCW. Hint #4 If Block 1 were shifted to the right, as the center of mass moves to the right of the fulcrum, it will create a CW torque that topples off Block 1. However, the small normal force from Block 2 has been decreasing as Block 1 moved to the right. Hint #5 The weight of Block 1 acts to the left of the fulcrum downwards, and the weight will produce a CCW torque, not CW. Hint #6 There is a normal force from Block 2 on Block 1 that acts to the left of the fulcrum upwards, producing a CW torque. Hint #7 Here is a diagram indicating the forces:

What is the equation for calculating torque?

torque = rFsin(angle)