Physics 112 Exam Math review

Waves

1. a) Find the frequency of a wave with a period that is 10.5 s/cycle.

b) If a wave's frequency is 3.6 cycles/s, what is its period?

2. Find the speed of a wave if it is 1.6 m from trough to crest and has a frequency of 14.8 Hz.

3. Identify the labelled parts in the following wave diagrams.

Sound

4. a) A wave of what length will resonate in a 65 cm long, 3 cm diameter closed tube?

b) Find the wave length if the tube is open.

5. a) If the Tair = 30⁰C, how long will it take a sound to echo from a wall 700 m distant?

b) If you hear an echo after 50s in 12⁰ air, what is the distance to the wall?

6. A 150 cm long string under 10 N tension vibrates at 2 500 Hz. At what frequency will it vibrate if shortened to 70 cm and retensioned to 15 N?

7. The Tair is 15⁰C when a lightning bolt is seen by a person 3 km away. The thunder clap will reach the person after how many seconds?

8. A car sounding its 2 500 Hz horn moves at 15 m/s toward a stationary listener. If the Tair = 20⁰ C, what frequency

is heard by the listener as the car:

a) approaches

b) passes

c) retreats.

Motion

9. a) An object accelerating at 6 m/s² will increase its speed from 2 m/s to 10 m/s in what time?

b) A 40 N push against a 50 N object causes what rate of acceleration?

c) What push is needed to just break the grip of friction if a 25 N box sits on a surface with a µ of 0.8. Now, if you push with 75 N against the box, how much of your push is excess?

d) An object moving at 3 m/s decelerates at 0.2 m/s² for 4 s. It will travel how far?

10. a) An object moves 400 m from 2 to 3.5 minutes. Find its average velocity.

b) Sketch a t-p story graph: object runs 3 m E in 15 s, pauses for 8 s, runs another 9 m E in 12 s, pauses for 15 s and then, in 25 s, runs back toward the reference but stops 3 m short. Hints: labels, units, scale, total time, total distance.

Forces, Friction

11. A 550 N sign hangs from the end of a rod sticking out from the side of a building. A support wire angles up at 30⁰ from the end to the rod to an attachment point in the building's wall. Find the tension in the rod and support wire.

12. a) A 40 kg box sits on a frictionless surface. It is attached to a 6 kg box hanging over the edge. Find the force trying to pull the two masses over the edge.

b) Find the common acceleration of the two boxes.

13. a) A 15 kg mass sitting on a surface and creates a µ of 0.9. It is attached to a 100 kg mass hanging over the edge. What force is trying to pull the two masses over the edge?

b) Find the force needed to overcome the grip of friction.

c) After friction, how much of the pulling force is extra?

d) Use the extra force to find the common acceleration of the two masses.

14. a) A 60 kg object sits on a 20⁰ slope. Find its weight component parallel to the slope.

b) Next, find its normal weight component.

c) Finally, if the object slides down the slope on its own, find the µ.

15. a) A 5 700 N strength rope is tied to a 100 kg cargo platform holding 350 kg of bricks. What is the maximum safe acceleration at which a crane operator can haul up the rope and its load?

b) If a winch pulls up a 6 200 N strength rope at 0.9 m/s², find the maximum total weight the rope can hold.

Momentum

16. a) A 6 kg object moving at 0.84 m/s collides with a stationary 2 kg porcupine. After the collision, they stick together and move on ahead as a unit. Find their common speed.

b) Two motionless objects face each other and then are blasted apart. If the 25 kg object on the left moves to the left at 0.3 m/s, what is the velocity of the 35 kg object on the right?

17. a) Find the PE of a 250 N object 5 m up.

b) Find the KE of a 400 g object moving at 1.2 m/s.

c) Find the speed that gives a 200 g object a KE of 10 J

18. a) Find the momentum of a 25 N object moving at 12 m/s.

b) What impulse does it receive from a 37 N force applied for 0.5 minutes?

c) Now, find the new momentum.

Energy, Work and Power

19. a) If you have a 100 W power rating, you can do how much work in 18 s?

b) You do what work to a crate if your 150 N push moves it 10 m across the floor?

c) Now, if your work is done in 26 s, what is your "power rating"?