Problem Set Physics I, Ejercicios de Física Avanzada

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James M. Hill

Physics 122 Problem Set

Mr. P. MacDonald

Introduction to Forces

1. Define inertia.
2. Describe inertial and gravitational mass.
3. Suppose a baseball and a table-tennis ball were traveling with the same velocity and you caught one in each hand – which would hurt more and why?
4. Forces break down in to which two groups? Give three examples of each.
5. Define and compare an object’s weight and mass.
6. In the formula for the force of gravity, how is the distance between masses accounted for?
7. Is the force of gravity acting on objects in Earth’s orbit?
8. Suppose you are on the ISS (which would be awesome), would you need to push a 50 kg object with a different force than a 100 kg object? Explain.

Force of Friction Review Questions

1. In the diagrams below, label the force of friction and normal force by the appropriate arrows.
2. Summarize what physical process causes friction.
3. How does friction depend on surface area between the two objects rubbing together? Think of a case where surface area could play a significant role in the force of friction.
4. Summarize the three situations when basic surface friction theory will not be applied.
5. Why will two identical pieces of smooth metals not fuse together?
6. What are the two types of friction? For two given surfaces which force of friction is greater?
7. Suppose you apply a force to a heavy object. Describe how the two forces of friction affect the object’s motion.
8. A textbook is sitting on a desk. Is there a force of friction present? Provide an explanation.
9. In what direction does friction always act?
10. Describe how heat is created when two surfaces are rubbed together.

Physics 112: Force Practice

11. A 6.2 kg book is pressed against the wall. The coefficient of static friction between the book and wall is 0.16. Calculate the minimum applied force necessary to keep the book from slipping down. (380 N)
12. A 14.7 kg box is pressed up against the wall using an applied force of 600 N. For the box not to fall, calculate the minimum coefficient of static friction necessary between the wall and the box. (0.24)
13. A 22 kg box held up against a wall. The coefficients of friction are μs = 0.39 and μk = 0.27. Calculate the minimum applied force necessary to support the box on the wall. After a period of time the applied force is 300 N, calculate the vertical net force on the crate. (554 N; 135 N [down])
14. A 15 kg box is pressed on a wall. The net force acting on the box is 294 N [down] when the horizontal pushing force is 275 N. Calculate the coefficient of kinetic friction. (0.32)

Newton’s First & Third Laws

7. Is the Earth an inertial frame of reference? If not, why are we still able to accurately use Newton’s laws of motion?
8. Give two examples of objects that cannot be analyzed with Newtonian mechanics.
9. Is the ball in the image below likely to land in the funnel if the cart is maintaining a constant velocity? What about if the cart has a constant acceleration? Provide an explanation for your answers.
10. Describe how the floor pushes you forward and that you do not push the floor.
11. How could an astronaut lost in space with a fire extinguisher move around?
12. Considering Newton’s 3rd^ Law, how is the horse able to move the cart?
13. Describe how Newton’s 3rd^ Law applies to rocket launches.

Chapter 5 page 159

Physics 112 Newton’s Laws Worksheet Mr. P. MacDonald

13. A car with a mass of 1550 kg is driving on track initially going 10 m/s. The driver accelerates to 30 m/s in

10 s. What is the average force acting on the car during that time? (F = 3100 N)

14. A car has a mass of 710 Kg. It starts from rest and travels 40 m in 3.0 s. What is the average force acting

on the car assuming a uniform acceleration? (F = 6300 N)

15. A force of – 9000 N is used to stop a 1500 kg car traveling 20 m/s. What breaking distance is needed to

bring the car to a halt? (d = 33 m)

16. A 65 kg diver jumps of a 10 m high platform.

a. Find the swimmer’s velocity the instant he reaches the water. (v = –14 m)

b. The swimmer comes to a stop 2.0 m below the surface of the water. Calculate the net stopping

force exerted by the water. (F = 3200 N)

17. A 825 kg car goes from 62 m/s [E] to 25 m/s [W] in 9.5 s.

a. Calculate the average force acting on the car. (-7555 N)

b. Calculate the final position of the car assuming the initial position is zero. (175 m [E])

c. Assuming a constant acceleration, calculate the instantaneous velocity 21 seconds (from when the

acceleration first started).

d. Calculate the final position of the car from part c.

e. Calculate the displacement of the car from the result of part b to d.

Connected Masses Practice

Calculate the acceleration of the masses and the magnitude of tension in the string in

the diagram below.

10.5 kg 14.1 kg

Given the information in the diagram, calculate M 2 and the magnitude of tension in the

string.

18 kg

a = 4.9 m/s^2

A counter weight of 13.5 kg is used to help a person of mass 62.4 kg do chin ups.

1. Calculate the force applied by the person if he accelerates at 1.9 m/s^2.

2. Calculate the magnitude of tension in the wire.

Physics 122: Vector Components

1. Calculate the horizontal,East, and vertical,North, components of the following vectors (East and

North are the positive directions). a. Fa = 248 N [E38oN] b. v = 65.6 m/s [W56oN] c. a = 38.4 m/s^2 [E81oS] d. FT = 614 N [W22oS] e. Δx = 1587 m [E33oN] f. a = 36.9 m/s^2 [W54oS]

2. Given the components of the following vectors, calculate the resultant vector.

a. FE = 21.4 N, FN = 38 N b. vE = -33 m/s, vN = 16 N c. FE = 87 N, FN = -66 N d. aE = -18 m/s^2 , aN = -9.5 m/s^2 e. vE = 45 m/s, vN = - 77 m/s f. vE = -159 m/s, vN = 121 m/s

Physics 122: Vector Components

3. Given the following three vectors, perform the indicated calculation. A = 35 m [E25oN], B = 61 m

[W66oN], and C = 50 m [E76oS] a. A + B b. A + C c. C – A d. 2 B – 3 C e. A + B + C f. A – B + C g. -2A + 5C

Physics 122: Applications of Vectors

1. If A = 35 m [E25oN], B = 43 m [E74oS], and C = 25 m [W45oS] Find: a. A + B b. 4A + 3C c. A – B d. 3C – 2B
2. What is the resultant displacement of 25 m [N], 18 m [S], and 12 m [E]? What is the average velocity if the trip took 37 seconds? {d = 13.9 m [E30oN]; v = 0.376 m/s [E30oN]}
3. Find the acceleration of an object that goes from 15.0 m/s [S] to 15 m/s [W] in 2.0 seconds. {a = 10.6 m/s^2 [W45oN]}
4. A car is initially moving 7.5 m/s [N]. After 3.0 seconds it is moving 10.0 m/s [E40oN]. Calculate: a. The acceleration. {a = 2.57 m/s^2 [E8.1oS]} b. The velocity after 6.0 s if the acceleration remains constant. {vf = 16.2 m/s [E19oN]}
5. What is the acceleration of a car that changes its velocity from 20.0 m/s [N] to 20.0 m/s [E45oN] in a time of 5.00 s? {a = 3.06 m/s^2 [E23oS]}
6. A 500 kg airplane in initially flying 200 m/s [E45oN] turns such that after 7.00 s the velocity is 140 m/s [E]. Find: a. The acceleration. {a = 20.2 m/s^2 [W89oS]} b. The average force acting during the turn. {F = 10100 N [W89oS]}
7. What is the force required to change to change the velocity of a 1200 kg car from 26.0 m/s [E] to 30.0 m/s [E30oS] in a time of 5.00 seconds? {F = 3600 N [S]}
8. Three forces act simultaneously on an object. One force is 10.0 N [N], the second is 15 N [W], and the third is 15.0 N [E60oN]. Determine the net force? {F = 24.2 N [W72oN]}
9. On a boat you are sailing 6.5 m/s [E20oS]. A gust of wind provides an acceleration equal to 2.1 m/s^2 [E60oN] for 18 seconds. a. What is your velocity after the 18 seconds? {v = 39.4 m/s [E51oN]} b. What is the displacement in during that time? {d = 378 m [E42oN]}
10. A glider is flying 9.2 m/s [E25oN]. A gust of wind changes the glider’s trajectory to 11 m/s [E14oS] in 7.9 seconds. a. What was the acceleration of the glider? {a = 0.88 m/s^2 [E70oS]} b. What was the displacement of the glider during that time? {d = 75 m [E3.7oN]} c. What was the average force if the glider has a mass of 55 kg? {F = 48 N [E70oS]]}
11. You are 37 km [W20oN] from Miramichi and must move to a position 15 km due West of the city. What displacement is required?{d = 23 km [E31oS]}

Physics 122: Applications of Vectors

12. A coast guard boat (with a helicopter) is 75 km [E67oN] from port. A distress call comes in from a fishing vessel located 93km [E26oS] from port. a. How far is the fishing boat from the coast guard boat? {d = 122 km [E64oS]} b. What is the minimum velocity of the helicopter to reach the boat in distress within 0.5 hours? {v = 244 km/s [E64oS]}
13. On a day when the wind is 80.0 km/h [E], an airplane is aimed [E65oN] and flown at a speed of 320 km/h. How far and in which direction will the plane fly in 0.33 hours? {d = 119 km [E53oN]}
14. A boat’s heading is directly across a river at 5.0 km/h. The river is flowing east at 3.0 km/h. a. What is the velocity of the boat relative to someone standing on the dock where the boat departed? {v = 5.8 km/h [E53oN]} b. How far down stream does it land if the trip takes 0.5 h? {dE = 1.5 km} c. How wide is the river? {dN = 2.5 km}
15. On a day when the wind is blowing 70 km/h [W40oS] you wish to fly to a destination 830 km [E60oS] in 1.5 hours. What heading and speed should you fly your plane? {v = 545 km/h [E53oS]}
16. A river has a current of 6.0 m/s [E]. What speed must a boat be able to travel to go straight across the river when it is aimed 75o^ upstream? {v = 23.2 m/s}
17. It is a distance of 500 m straight east to get across a river. The river has a current of 3.7 m/s due south. You have a boat that can travel 10 m/s. a. Which way should you aim your boat to get directly across the river? {E22oN} b. How long will it take to cross the river? {54 s}
18. A boat can travel 7.5 m/s. Which way must it be aimed to travel directly across a river with a current of 3.6 m/s? {29o^ upstream}
19. A Canadian submarine is 185 km [E22oS] of Halifax. An enemy sub is spotted 425 km [E67oN] of Halifax. The enemy is heading directly towards Halifax at 45 km/h. What minimum velocity is required for the Canadian submarine to intercept the enemy sub 200 km from Halifax? {vsub = 54 km/h [W70oN]}
20. An object is moving 35 m/s [E40oN] and undergoes an acceleration of 3.7 m/s^2 [W10oN]. How much time is required for the displacement to be 609 m [W72oN]? {t = 20 s]
21. Given the information below, solve for the missing vector:

Physics 122: Projectile Problems

2. A ball bearing traveling with constant speed rolls off a lab bench that is 0.928 m high. If it hits the ground 0.422 m from the edge of the bench, how fast was the ball bearing rolling across the table initially? (0. m/s)
3. Johnny shoots a stone horizontally with a velocity of +25 m/s from his slingshot while standing on the roof of a building on his father’s farm. When he dropped an identical stone from the same spot, it took 1.85 s to hit the ground. What was the height of the building? (16.8 m)
4. A stone is thrown horizontally from a cliff 15.0 m high. a) The initial velocity is +24.0 m/s. How far from the base of the cliff does the stone strike the ground? (42.0 m) b) What is the final vertical velocity of the stone just before the stone hits the ground? (-17.1 m/s) c) Calculate the velocity of the stone just before the stone hits the ground? (29.5 m/s, 35.5o^ S of E)
5. A cannonball is fired from a cannon. If the initial horizontal and vertical components of the velocity are +32 m/s and +27 m/s respectively, at what angle was the cannon ball launched and at what speed was it fired? (40o^ to the horizontal, 42 m/s) How long will the cannonball be in the air? (5.5 s)
6. A projectile fired at an angle remains in the air for 8.42 s after it is fired. The initial horizontal component of its velocity is +150 m/s. a) How far forward did the projectile move forward before it hit the ground? (1.26 x 10^3 m) b) How long after being fired did it reach its maximum height? (4.21 s)
7. A ball is thrown from the top of one building toward the wall of a second taller building 15.2 m away. The ball is thrown with an initial velocity of 6.10 m/s at an angle of 40.0o^ to the horizontal. How far below its original position does the ball hit the second building? (39.1 m below its original position)
8. A baseball player throws a ball from center field to home plate with a velocity of 35.0 m/s at an angle of 30.0o^ with the ground. Assuming the ball is caught at the same height at which it was thrown; calculate the horizontal distance traveled by the ball before it is caught. (108 m)
9. A projectile is fired with an initial velocity of 75.2 m/s at an angle of 34.5o^ above the horizontal along a long flat firing range. Determine the a) maximum height reached by the projectile (92.7 m) b) range of the projectile (539 m) c) speed of the projectile 1.50 s after being fired (68.0 m/s)
10. A hockey player hits a puck with his hockey stick and the puck is launched at an angle of 45o^ to the ice surface. The puck hits the ice 35 m down the length of the rink. Find the velocity of the puck when it left the hockey stick. (19 m/s at 45o^ to the horizontal)

Physics 122: Projectile Problems

11. A no good thief steals Mrs. Corlette’s purse and makes a run for it. Mrs. Corlette, being puny and weak, calls for help. Mr. MacDonald sees this happen and gets angry, turns green, muscles rip his shirt apart, and he wants to smash. Mr. MacDonald becomes thePhulk and grabs a nearby car at the spot the purse was stolen and throws it East at an angle of 45o^ to the horizontal. The instant the doomed car left the Phulk’s hand the thief has run for 8.7 seconds at a constant velocity of 3.2 m/s [E]. With what initial speed does the Phulk have to throw the car so that it hits the running thief? (19 m/s)
12. A cannonball has a muzzle speed of 35 m/s. If the cannon ball is launched from the ground then what is the maximum range of the cannonball? (125 m)
13. Suppose the cannon from #12 were placed on a 17 m high castle wall. What is its new maximum range? ( m)
14. How high should the cannon from #12 be placed to pulverize advancing orcs that are 200 m away; assuming that 200 m is the maximum range of the cannon? (120 m)
15. The King, fed up with stupid, ugly orcs, wants to increase the maximum range of his cannons to 500 m. The cannons are placed 25 m up in the castle. What muzzle speed should the cannonballs have? (68.3 m/s)
16. MHR Page 549 PP #14. Go ahead, try it. I double-dog dare ya.

Chapter 11 Pg 543