Description

Vector components and free body diagrams

Two essential concepts you were learning in the course up to this point were determining the components of a vector and drawing a free body diagram that represents the forces acting on an object.

Question 1: For each of the following, determine the components that make up the resultant vector.

1. ∣∣

   ?

   ⇀
   ?∣∣

   =40?

   F⇀g=40N

   
   

   

2. v⃑ 

   =25

   ??

    [?15°?]

   v⃑=25ms [N15°E]

   
   

   

3. A person throws a ball with an initial velocity of 16 m/s, 65° above the horizontal.

   

Question 2: For each of the following draw a free body diagram that includes all of the forces acting on the object described.

1. A 40 kg box on a level floor is pulled by a rope attached to the box. The ropes makes an angle of 21° with the horizontal. A force of friction opposes the motion.
2. A refrigerator sits on a level floor and a person tries to push on it with a force parallel to the floor. The refrigerator does not move.

Task 2: Relative velocity and projectile motion problem solving

For the problems below, complete the procedural instructions for each problem.

Question 1: A helicopter flies with an airspeed of 42.5 m/s [W]. If the wind is traveling with a velocity of 25.0 m/s [E30°S] relative to the ground then determine the velocity of the helicopter relative to the ground.

1. Use the data from the question to determine the velocity components for the helicopter’s speed relative to the air and the wind’s speed relative to the ground.
2. Use your velocity components from part (a) and determine the resultant velocity for each component. (In other words, determine the resultant horizontal component for the helicopter’s ground speed and the resultant vertical component for the helicopter’s ground speed).
3. Using your data, determine the resultant velocity of the helicopter relative to the ground.

Question 2: A golf ball is hit from 4.3 m above a golfing fairway with an initial velocity of 30.0 m/s at an angle of 35° above the horizontal.

1. Determine the time of flight for the ball.
2. Determine the range for the golf ball.
3. Determine the velocity for the golf ball the instant before the ball impacts the ground.

Task 3: Newton’s laws of motion and uniform circular motion problem-solving

Answers must include a full solution process. Your final answer must include the correct final units and the correct significant figures.

Question 1: A 120 kg piano is at the top of a ramp that makes an angle of 30° with the level ground. As the piano slides down the ramp it experiences a force of friction. The coefficient of kinetic friction is 0.10.

1. Draw free body diagram that represents the forces acting on the piano.
2. Determine the magnitude of the normal force acting on the piano.
3. Determine the magnitude of the kinetic force of friction acting on the piano.
4. Determine the acceleration of the piano along the axis parallel to the ramp (i.e. what is the acceleration down the ramp?).

Question 2: Keys with a combined mass of 0.100 kg are attached to a 0.25 m long string and swung in a circle in the vertical plane.

1. Determine the slowest speed that the keys can swing and still maintain a circular path.
2. Determine the magnitude of the tension in the string at the bottom of the circle.

Question 3: Two objects are connected by a string passing over a frictionless pulley. When the objects are in motion object A experiences a force of kinetic friction with a magnitude equal to 5.0 N. The mass of object A is 2.1 kg and the mass of object B is 3.3 kg.

1. Determine the magnitude of acceleration for the system.
2. Determine the magnitude of the tension in the string.