LECTURE CH 5 FORCE PROBLEMS 4/8/08, 2:17 PM PAGE 1 OF 25 Name______
Example 5.2 “Readying a wrecking ball”
(a) RECOPY THE FBD. Work with force magnitudes. T1, T2, W = M g What is a magnitude?
· Identify the unknown magnitudes.
(b) Use trigonometry to write the X and Y components of each of the three forces. Get your answers to 3 significant figures.
(c) Use Newton’s 2nd Law (for static equilibrium) to generate 2 equations in 2 unknowns. The 2 unknowns are T1 and T2.
(d) Solve the equations for part (c).
Example 5.2 “Readying a wrecking ball” according to abe’s variation
(a) Review of tension force “T” in a rope (4 possible tension forces!!)
· Consider a vertically hanging wrecking ball on a rope.
What are the four tension forces associated with the rope?
Make a FBD for the just the wrecking ball. What is the magnitude of the tension force on the ball? (2500. N)
(b) Let’s redraw the free body diagram for just the ball.
· Write down Newton’s 2nd Law equations for static equilibrium
Note the difference between “force magnitudes” and “force components”
Equation 1 X equation - T1 + T2 sinq + 0 = 0
Equation 2 Y equation 0 + T2 cosq + (- 2500. N) = 0
We have 2 simultaneous equations. Solve (8th grade)
T2 = 2.66 x 103 N
T1 = 910. N
IN CLASS PROBLEM Example 5.3 Tension in towing a car at a constant velocity (zero acceleration or “dynamic equilibrium”) Note: Fnet = 0 even though the car is in moving!!
(a) What is a magnitude?
· Re-sketch the free body diagram using only force “magnitudes and angles.”
(b) Use trigonometry to write the X and Y components of each of the four forces. Get your answers to 3 significant figures. What is the difference between a magnitude and a component?
(c) Make a motion diagram for the car.
(d) Use Newton’s 2nd Law to generate 2 equations in 2 unknowns. The 2 unknowns are N and T. Solve the equations for the unknowns.
Example 5.3 Tension in towing a car at a constant velocity (zero acceleration or “dynamic equilibrium”) Note: Fnet = 0 even though the car is in moving!!
(d) Solve the equations for part (c).
#1 X equation T cosq + (- 320. N) + 0 + 0 = 0 T = 341. N
#2 Y equation T sinq + 0 + n + (- Wt) = 0 n = 1.46 x 104 N < Wt
IN CLASS PROBLEM
Example 5.5 Tension in towing a car with constant acceleration (not in equilibrium!)
(a) What is a magnitude? Re-sketch the free body diagram using only force “magnitudes and angles.”
(b) Use trigonometry to write the X and Y components of each of the four forces. Get your answers to 3 significant figures. What is the difference between a magnitude and a component?
(c) Make a motion diagram for the car.
(d) Use Newton’s 2nd Law to generate 2 equations in 2 unknowns. The 2 unknowns are N and T. Solve the equations for the unknowns.
Find the tension T in the rope.
· Draw motion diagram
· Draw free body diagram
Note force magnitudes (+) T, f, n, Wt Wt = 1500.· 9.80 = 1.47 x 104 N
Note force components (+) Tx, Ty, fx, fy, nx, ny, Wtx, Wty
#1 X equation T cosq + (- 320. N) + 0 + 0 = M aX
find aX = DVX / Dt = 1.20 m/s2 T = 2.26 X 103 N
Note: If you have time, use the Y equation to find the normal force magnitude n.
#2 Y equation T sinq + 0 + n + (- Wt) = M aY
· Calculate the "weight" and "mass" for each of the following. Give your answer in both BE and SI units. [HRF3,5-15E]
(a) a 5.00 pound bag of sugar.
(b) a 240. lb fullback.
(c) a 1.80 ton automobile.
· A man “weighs” 800. N.
(a) Determine his weight and mass in SI units.
(b) Determine his weight and mass in BE units.
(c) Determine his weight and mass in CGS units.
Example 5.2 “Readying a wrecking ball”
Example 5.2 “Readying a wrecking ball” according to abe’s variation
(c) Review of tension force “T” in a rope (4 possible tension forces!!)
· Consider a vertically hanging wrecking ball on a rope.
What are the four tension forces associated with the rope?
Make a FBD for the just the wrecking ball. What is the magnitude of the tension force on the ball? (2500. N)
(d) Let’s redraw the free body diagram for just the ball.
· Write down Newton’s 2nd Law equations for static equilibrium
Note the difference between “force magnitudes” and “force components”
Equation 1 X equation - T1 + T2 sinq + 0 = 0
Equation 2 Y equation 0 + T2 cosq + (- 2500. N) = 0
We have 2 simultaneous equations. Solve (8th grade)
T2 = 2.66 x 103 N
T1 = 910. N
· You are walking on the floor in the positive X direction. Study the following figure (4.35 a from MP) and then answer the questions.
(a) Make a diagram which shows all forces on your body, the floor, and the earth as you are walking.
(b) Make a FBD of your body as it is walking.
(c) What is the origin of the force which causes you to move forward?
· Example 5.15 Pushing two blocks. (VARIATION) Figure 5.33 shows a 5.00 kg block A being pushed with a 3.00 N force. In front of this block is a 10.0 kg block B; the two blocks move together. (Do all calculations to 3 sig figs.)
(a) Make an FBD of the combined system.
(b) Use N-2 to obtain the acceleration of the combined system.
(c) Make an FBD for just block A.
CONTINUED Example 5.15 Pushing two blocks. Figure 5.33 shows a 5.00 kg block A being pushed with a 3.00 N force. In front of this block is a 10.0 kg block B; the two blocks move together. (Do all calculations to 3 sig figs.)
(d) Use N-2 to find the force magnitude Fon B by A on block B by block A?
(e) Make an FBD for just block B.
(f) Use N-2 to find the force magnitude Fon A by B on block A by block B?
Example 5.3 Tension in towing a car at a constant velocity (zero acceleration or “dynamic equilibrium”) Note: Fnet = 0 even though the car is in moving!!
· Sketch free body diagram
Note force magnitudes (+) T, f, n, Wt Wt = 1500.· 9.80 = 1.47 x 104 N
Note force components (+) Tx, Ty, fx, fy, nx, ny, Wtx, Wty
#1 X equation T cosq + (- 320. N) + 0 + 0 = 0 T = 341. N
#2 Y equation T sinq + 0 + n + (- Wt) = 0 n = 1.46 x 104 N < Wt
Example 5.5 Tension in towing a car with constant acceleration (not in equilibrium!)
Find the tension T in the rope.
· Draw motion diagram
· Draw free body diagram
Note force magnitudes (+) T, f, n, Wt Wt = 1500.· 9.80 = 1.47 x 104 N
Note force components (+) Tx, Ty, fx, fy, nx, ny, Wtx, Wty
#1 X equation T cosq + (- 320. N) + 0 + 0 = M aX
find aX = DVX / Dt = 1.20 m/s2 T = 2.26 X 103 N
Note: If you have time, use the Y equation to find the normal force magnitude n.
#2 Y equation T sinq + 0 + n + (- Wt) = M aY
· A box of books is initially at rest on a floor. The mass of the box is 90.0 kg. The coefficients of static and kinetic friction for the bottom of the box and the floor are µs = 0.700 and µk = 0.600 . Let the applied force Fapp on the box be horizontal in the positive X direction.
(a) On the above figure, sketch and label the forces (which only act) on the box.
(b) Calculate the magnitude of the normal force.
(c) For the following table, calculate the magnitude of the friction force and state whether the box is moving or not.
Fapplied Friction Force Does box move ? If so, what is the acceleration aX?
Show work on back if more space is required.
______
0 N
______
50 N
______
100 N
______
250 N
______
400 N
______
600 N
______
650 N
______
700 N
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A box of mass M = 15.0 kg is motionless on a rough inclined plane at an angle of 35.0 degrees with respect to the horizontal. The coefficient of static friction for the box and plane is .800. Hint: Use tilted coordinate system for this problem.
(a) Illustrate all forces acting on the box.
(b) On a diagram, show the x and y components of the gravitational force. Also, calculate these components. (84.4 N, -120. N)
(c) Use the equilibrium condition for y-components of force to calculate the magnitude of the normal force.
(d) Calculate the magnitude of the friction force.
(e) If the mass of the box is increased sufficiently, will it start to slide ?
(f) At what angle will the box start to slide?
· You are given the earth and the moon.
(a) Make a diagram showing gravitational interaction forces between the earth and the moon. Label the forces appropriately.
(b) Look up the masses of the earth and moon and also their separation distance.
Mearth = Mmoon = rseparation =
(c) Calculate the gravitational force between the earth and the moon.
(d) Calculate the “weight” force on a 70.0 kg person standing on the earth’s surface. Use SI units and 3 sig figs.
· Use the standard method.
· Use Newton’s Law of Universal Gravitation to get the same answer! Hint: Look up the radius of the earth first!
(e) Challenge: How far from the center of the earth will the net force on the person be zero?
Two types of forces continued
· 2. Action at a distance forces force seems to act through “empty space”
o Gravitational force Weight = “Wt” = M g
o Electric and magnetic forces
Fundamental particles electron, proton, neutron
More fundamental proton and neutron are composites of quarks
o Nuclear (strong) and nuclear (weak) forces
Newton’s Law of Universal Gravitation Fundamental Law of Gravity between any two objects in the universe (includes Solar System and beyond. The force seems to have an infinite range. This is an exact law with only tiny corrections from General Relativity.
What is the relation between G and g = 9.80 m / s2 ?
Consider the gravitational force on a basketball at the surface of the Earth.
Memorize: Newton’s Laws and corresponding formulas; formulas for static and kinetic friction forces.
MORE Optional HOMEWORK PROBLEMS WITH ANSWERS All SI, BE, and CGS units defined until present assignment.
(1) A constant force of 3.75 N is applied to a hockey puck in the positive x-direction. (Note: A hockey stick remains in contact with the puck in order to apply the constant force.) The puck is initially at rest at the origin; its mass is .150 kg. Assume there is no friction between the puck and the ice. (a) What is the acceleration in the x-direction ? (b) At what time t will the puck have a speed of 5.20 m/s ? (c) How far has the puck moved at the time from part (b) ? [HRF3,5-4E] ( 25.0 m/s2, .208 s, .541 m )
(2) A 200 kg boat is being pulled in the water by two ropes. The first rope exerts a force magnitude F1 of 700. N in the positive x-direction; the second rope exerts a force magnitude F2 of 900 N at an angle of 30.0 degrees CCL with respect to the positive x-direction. (a) Make a vector diagram which illustrates the two forces and their resultant force FR . (You may wish to use the “parallelogram rule”.) (b) Calculate the x and y components of FR. (c) Calculate the x and y components of the acceleration vector of the boat. (d) Calculate the magnitude and angle of the acceleration vector. (e) Assuming the boat starts from rest, find where its coordinates after 8.00 s and the distance which it has moved. (1.48 . 103 N, 450. N, 7.40 m/s2, 2.25 m/s2, 7.73 m/s2, 16.9 degrees CCL WRT + x direction, 237.,72.0, 247.)
(3) Given a 5 kg box which is resting on the surface of the earth. (a) Make a free body diagram of the box. Sketch and label all forces which act on the box. (b) Calculate the magnitude of each force acting on the box. (c) Make a “cartoon” sketch of the box sitting on the earth. Illustrate action and reaction pairs.
(4) Given a 5 kg box which is hanging by a rope. (a) Make a free body diagram of the box. Sketch and label all forces which act on the box. (b) Calculate the magnitude of each force acting on the box. (c) Sketch the box hanging from the ceiling. Illustrate action and reaction pairs.
(5) A woman is walking on the floor. What is the origin of the force which causes her to move forward? Make a sketch to illustrate.
(6) Calculate the "weight" and "mass" for each of the following. Use SI units for your answer. (a) a "5.00 lb" bag of sugar. (b) a "240 lb" fullback. (c) a "1.80 ton" automobile. [HRF3,5-15E] (22.2 N, 2.27 kg, 1.07x103 N, 109. kg, 1.60x104 N, 1.63x103 kg)
(7) A man “weighs” 150 lbs. (a) Calculate his weight and mass in SI units. (b) Calculate his weight and mass in BE units. (c) Calculate his weight and mass in CGS units.
WAIT (8) Sketch and calculate the magnitudes of the tension forces for each of the following ? Let M = 5 kg. Assume frictionless and massless pulleys. (49.0 N, 24.5 N, 24.5 N) Can you design a system which reduces the tension below 15 N. See “Solved Problem 1” in Cutnell and Johnson.
(9) An automobile which weighs 3800 lbs is accelerating at 12.0 ft/s2 along the positive x-axis. (a) Calculate the mass of the automobile in British units. (b) Calculate the force on the automobile in British units. (c) What is applying the force to move the automobile? [HRF3,5-20E] (119 slugs, 1.43x103 lbs, to be discussed in class)