# 1 What force is required to accelerate an automobile with a mass

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```							Force Problem Bank 1. Basic Force Problems 1.1. What net force is required to accelerate a 1500 kg automobile at 3 m/s2? 1.2. A body of mass 2 kg is acted upon by an unbalanced force of 6 N. Find the acceleration. 1.3. A horizontal force applied to a 24 kg mass will give it an acceleration of 5.8 m/s2. Find the magnitude of the force. 1.4. What net force is required to accelerate a 2000 kg car from 5 m/s to 25 m/s, in a time of 5 s? 1.5. A 6 kg object undergoes an acceleration of 2 m/s2. (a) What is the magnitude of the unbalanced force acting on it? (b) If the same force were applied to a 4 kg object, what acceleration will be produced? 1.6. The engine on a 0.2 kg model airplane exerts a forward force on the plane of 10 N, while the air exerts a resistive force of 7.5 N. If these are the only horizontal forces acting on the plane, what is the horizontal acceleration of the plane? 1.7. A moving cart is pushed from behind with a force of 10 N. The retarding forces of friction and air resistance equal 2 N. If the mass of the cart is 1.5 kg, what is its acceleration? 1.8. A football m/s during 0.2 s). If unbalanced punter accelerates a football from rest to a speed of 10 the time his toe is in contact with the ball (about the football has a mass of 0.5 kg, what average force is exerted on the ball?

1.9. What unbalanced force acting on a body having a mass of 27 kg will: (a) give it an acceleration of 2.4 m/s2? (b) give it a speed of 7.3 m/s in 6 s from rest? (c) cause it to move 30 m in 5 s from rest? (d) increase its speed from 2 m/s to 7 m/s in 5 s? (e) change its speed from 19 m/s to 10 m/s while passing through a distance of 29 m? 1.10.A bullet of mass 15 g leaves the barrel of a rifle with a speed of 800 m/s. If the length of the barrel is 75 cm, determine the average unbalanced force (in Newtons) that accelerates the bullet. 1.11.A jet plane, loaded with passengers, has a mass of 1.25 x 105 kg. If, with this load, the plane requires a speed of 60 m/s for take off on a 2000 m runway, find (a) the acceleration required, (b) the time the wheels leave the ground, (c) the unbalanced force needed to get the plane off the ground. 1.12.A force of 5 N gives a mass m1 an acceleration of 8 m/s2, and a mass m2 an acceleration of 24 m/s2. What acceleration would it give the two when they are fastened together?

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Force Problem Bank 1.13.A block of mass 8.0 kg, starting from rest, is pulled along a horizontal table top. It is found that this body moves a distance of 3.0 m in 6.0 s. (a) What is the acceleration of the body? (b) What is the magnitude of the net force? 1.14.A hockey puck with a mass of 0.25 kg slides along the ice for 50 m before it stops. If its initial speed was 20 m/s, what is the force of friction between the ice and the puck? 1.15.A 25 g golf ball, moving with a speed of 40 m/s, lands in a sand trap and becomes embedded a distance of 8 cm. Assuming constant acceleration during impact, find: (a) the time required for the ball to stop, (b) the average unbalanced force. 1.16.A 5 kg artillery shell traveling at 900 m/s strikes a hillside and penetrates the ground to a depth of 2 m. (a) Find the time of stopping. (b) Find the average unbalanced force acting on the shell causing it to stop. 1.17.A net force of 10 N pulls horizontally on a 2 kg mass (starting from rest) and pulls for 10 seconds. Then the forward force is removed, leaving only a resistive force. The mass decelerates to a stop in a distance of 150 m from where the forward force was removed. (a) Find the speed at the end of 10 s. (b) What force acts on the mass as it slows down? 1.18.A model airplane motor exerts a forward force of 2 N on a 0.2 kg plane. (a) Ignoring air resistance, determine the distance the plane will fly in 5 s if it starts from rest. (b) If the movement of the plane gives rise to a resistive force due to air resistance of 1.5 N, what distance will the plane cover in 5 s? 1.19.A 50 kg cart is being towed by a lawn tractor using a horizontal chain. If the tractor accelerates from rest to a speed of 10 m/s in 2 s, what force is exerted on the tractor? Ignore friction. 2. Problems That Include Weight 2.1. A proton has a mass of 1.672 x 10-27 kg. What is its weight? 2.2. On Planet X, a 50 kg barbell can be lifted with a force of 180 N. (a) What is the acceleration due to gravity on Planet X? (b) If the same barbell is lifted on earth, what force is needed? 2.3. What braking force is needed to stop an automobile with a weight of 19,600 N from a speed of 90 km/hr in 4.5 s?

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Force Problem Bank 2.4. A 1500 kg car starting from rest undergoes an acceleration of 2.5 m/s2 for 8 s, then an acceleration of 1.5 m/s2 for 10 s. Find: (a) the weight of the car, (b) the force applied during the first 8 s, (c) the force applied during the second acceleration, (d) the total distance traveled, (e) the average velocity.

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Force Problem Bank 3. Elevators And Similar Problems 3.1. An elevator has a mass of 2900 kg. Determine the tension in the cable under the following conditions: (a) The elevator starts upward from the ground floor with an acceleration of 1.1 m/s2. (b) The elevator comes to a stop at the top floor with an acceleration of 1.1 m/s2 down. (c) The elevator starts downward from the top floor with an acceleration of 1.1 m/s2. (d) The elevator moves downward at a constant speed of 1.1 m/s. (e) The elevator comes to a stop at the ground floor with an upward acceleration of 1.1 m/s2. 3.2. A vertical rope is attached to a 600 kg boulder. What is the tension in the rope which causes the boulder to have an upward velocity of 2.8 m/s at an instant 0.6 s after leaving the ground? 3.3. A crane lifts a load of 5000 kg. The magnitude of the acceleration in cases a to d below is 1.8 m/s2. Find the tension in the cable for all cases. (a) The load starts upward from rest on the ground. (b) The load comes to a stop after rising 30 m. (c) The load starts downward from a height of 30 m. (d) The load comes to a stop after dropping 15 m. (e) The load drops at constant speed. 3.4. A 23 kg block hangs at the end of a rope. Find the acceleration of the block if the tension in the rope is: (a) 225.4 N (b) 178.2 N (c) 334 N 3.5. What upward force must be exerted on a 2 kg mass to cause it to rise with an acceleration of 1.2 m/s2? 3.6. A 2 kg mass hangs from a wire. Find the tension in the wire under these circumstances: (a) Under an acceleration of 5 m/s2 up. (b) Under an acceleration of 5 m/s2 down. (c) Does the direction of motion matter in solving parts a and b? 3.7. A man, weight = 890 N, stands on a bathroom scale in an elevator. What does the scale read when the elevator is (a) at rest? (a) rising with a constant speed of 1.3 m/s? (c) starting upward with a constant acceleration of 1.3 m/s2. (d) starting downward with a constant acceleration of 1.3 m/s2.

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Force Problem Bank 4. Objects Connected By Strings 4.1. Two barrels of masses 4 kg and 7 kg are pulled along a frictionless surface of a frozen pond by an ice fisherman. If he exerts a force of 30 N on the first barrel, determine the acceleration of the system and the tension in the cord connecting the barrels. 4.4. Two masses, each 4 kg, are connected by a light cord over a frictionless pulley. One mass is free to slide on a frictionless horizontal surface and the other falls vertically. Calculate the acceleration of each mass and the tension in the cord.

4.2. A mass of 800 g is suspended from a light cord and a mass of 1200 g is suspended under it by another cord. Calculate the tension in each cord when the masses: (a) start upward with an acceleration of 4 m/s2, (b) start downward with an acceleration of 4 m/s2.

4.5. A 10 kg mass sitting on a frictionless table is connected by means of a string and pulley to a 5 kg mass hanging over the edge of the table. What is the acceleration of the mass and the tension in the string? 4.6. A 10 kg mass is attached to a cord that passes over a light frictionless pulley to another 10 kg mass on the other side. A 5 kg mass is attached by a cord to the bottom of one of the 10 kg masses. (a) What is the acceleration of the system? (b) What is the tension in each cord?

4.3. A cord passing over a pulley has a 7 kg mass tied to one end and a 9 kg mass tied to the other. Determine the acceleration of the system and the tension in the cord.

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Force Problem Bank 4.7. The 1.5 kg block shown below starts at rest and hits the floor in 0.95 s. (a) Find the acceleration of the 1.5 kg block. (b) Find the mass m. (c) Find the tension in the string. 4.9. The 4 kg mass falls 1 m in 1.2 s. Find the value of the second mass x.

x

4 kg

4.8. (a) What would be the acceleration of the 1 kg mass below, and the tension in the string? (b) How long would it take (starting from rest) to fall one meter? (c) If the 1 kg and 3 kg masses were exchanged, what would be the acceleration and tension in the string?

4.10.A locomotive pulls six freight cars, each having a mass of 10,000 kg and each experiencing a frictional resistance of 1200 N. The locomotive accelerates the train at 0.50 m/s2. (a) What is the tension in the coupling between the locomotive and the first freight car? (b) What is the tension in the coupling pulling the last freight car?

5. Static Equilibrium Problems

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Force Problem Bank 5.1. A weight is hanging from two cords as shown below. Find the tension in the two cords, F1 and F2. 5.4. Find the tension in the cable and the push of the rod.

5.2. Find the tension in the two cords, F1 and F2. 5.5. A sign of weight = 500 N is supported as shown. Find the magnitude and direction of the forces supplied by the cable and rod

5.3. Find the tension in the two cords, F1 and F2.

FT

40°

FP

mg

Eat At Joe ’s

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Force Problem Bank 5.6. A weight of 7000 N is supported by the hoist shown below. Find the push force supplied by the boom and the tension in the horizontal cable 5.7. A rectangular picture frame weighing 4 N is supported by a wire attached to its top corners and passed over a nail in the wall. Each wire makes a 45° angle with the horizontal. What force is supplied by each half of the wire? 5.8. A street lamp weighs 190 N. It is supported equally by two wires that form an angle of 110° to each other. Find the tension in the wires.

6. Friction 6.1. A force of 120 N is required to move a 75 kg crate across a warehouse floor at constant velocity. (a) What is the force of friction on the crate? (b) What is the normal force on the crate? (c) What is the coefficient of friction between the crate and the floor? 6.2. When a small box, mass = 0.30 kg, is pushed with a force of 2.0 N across a lab table, it accelerates at a rate of 0.85 m/s2. (a) What is the force of friction on the box? (b) What is the normal force on the box? (c) What is the coefficient of friction between the box and the lab table? 6.3. The coefficient of friction between a 48 kg crate and the floor is 0.32. What force is required to move the crate at constant velocity across the floor? 6.4. A 150 kg crate is pushed horizontally with a force of 500 N. If the coefficient of friction is 0.25, what is the acceleration of the crate? 6.5. A force of 45 N gives a 6.2 kg block an acceleration of 3.7 m/s2. What is the coefficient of friction between the block and the table? 6.6. A box sliding at 8 m/s comes to a rest in a distance of 12 m. What is the coefficient of friction?

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Force Problem Bank 6.7. A loaded sled of mass 70 kg is pushed onto the flat frozen surface of a lake with an initial velocity of 12 m/s. How far does the sled travel before stopping if the coefficient of friction between the ice and the runners is 0.05? 6.8. A block with a mass of 45 kg rests on a rough horizontal floor. The coefficient of kinetic friction between the block and the floor is 0.25. A horizontal force of 178 N acts on the block for 3 s. Compute the velocity of the block at the end of the 3 s interval. 7. Wagon And Lawnmower Problems 7.1. A child exerts a 60 N force on a wagon handle at an angle of 25° from the horizontal. What are the horizontal and vertical components of this force? 7.2. A pickup truck pulls on a stump using a chain at angle of 15° from the horizontal. If the truck exerts a force of 1400 N, what are the horizontal and vertical components? 7.3. Two movers attempt to move a 50 kg piece of equipment by exerting forces of 200 N north and 300 N east. (a) What is the resultant force acting on the piece of equipment, assuming that friction can be ignored? (b) What are the magnitude and direction of the acceleration on the object? (c) If the 300 N force is exerted at an angle of 40° N of W, find the resultant force and acceleration. 7.4. A 20 kg wagon is pulled by a 10 N force at an angle of 30° to the horizontal. Ignore friction. (a) Find the acceleration. (b) Find the normal force. 7.5. A gardener pushes down along the handle of a lawn mower of 20 kg mass with a force of 150 N. The handle makes an angle of 60° with the ground. The force of friction is 25 N. What is the acceleration of the mower? 7.6. A man pushes a supermarket cart of mass 15 kg with a horizontal force of 30 N. Friction is negligible. (a) What acceleration does the cart experience? (b) Calculate the acceleration assuming that the 30 N force is applied at a 30° angle downward from the horizontal. 7.7. A woman puts a 35 N force on the handle of a 42 kg lawnmower. The handle makes an angle of 50° with the ground. The force of friction is 20 N. Find the acceleration of the lawnmower. 7.8. What is the force of friction on a box being pulled across a floor at constant speed by a rope at a 35° angle to the horizontal, if the applied force is 120 N?

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Force Problem Bank 7.9. A man uses a rope to drag a package across the floor with a force of 40 N. The mass of the package is 10 kg. If the acceleration is 3.5 m/s2, and friction can be ignored, what is the angle up from the horizontal of the rope? 7.10.A 25 kg box is dragged across the floor with a force of 100 N applied at a 40° up from the horizontal. The coefficient of friction is 0.32. (a) What is the normal force? (b) What is the force of friction? (c) What is the acceleration of the box? 7.11.A wagon is pulled by a boy at constant speed using a handle with an angle of 45° to the horizontal. The mass of the wagon is 38 kg. If the applied force is 40 N, find (a) the normal force, (b) the force of friction, (c) the coefficient of friction. 7.12.A girl pulls a 40 kg crate across a level floor with a force of 180 N. If the force acts at an angle of 30° up from the horizontal, and the coefficient of friction is 0.25, find (a) the normal force, (b) the force of friction, (c) the acceleration of the crate. 7.13.A lawnmower is pushed at constant speed using a handle with an angle of 45° to the horizontal. The mass of the lawnmower is 15 kg. If the applied force is 25 N, find (a) the normal force, (b) the force of friction, (c) the coefficient of friction. 7.14.A loaded sled has a mass of 1650 kg. It is pulled at constant speed along a level road by a force of 400 N applied to a rope which is 25° up from the horizontal. Find (a) the force of friction, (b) the normal force, (c) the coefficient of friction. 7.15.A woman pushes a crate along the floor of a warehouse with a force of 40 N directed downward at an angle of 20° from the horizontal. If the crate has a mass of 60 kg and the coefficient of friction is 0.05, find (a) the normal force, (b) the force of friction, (c) the acceleration.

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Force Problem Bank 7.16.A worker pushes on a box with a force of 90 N at an angle of 25° down from the horizontal. The box has a mass of 20 kg and the coefficient of friction is 0.08. Find (a) the normal force, (b) the force of friction, (c) the acceleration. (d) If the box moves 1.2 m, what is the final velocity? 8. Inclined Plane Problems 8.1. (a) Find the acceleration of the mass, assuming friction may be ignored. (b) Find the length of the incline, if the mass starts from rest and has a final velocity of 24 m/s. (c) Find the amount of time it takes the mass to slide down the incline.

8.2. Find the acceleration of the mass if the coefficient of friction is 0.10.

8.3. What push directed along a 30° smooth incline is necessary to give a 40 kg cart an acceleration of 2 m/s2 up the incline? 8.4. The coefficient of friction between a metal block and the inclined surface over which it will slide is 0.20. If the surface makes an angle of 20° with the horizontal and the block has a mass of 80 kg, what force is required to slide the block at uniform speed up the plane?

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Force Problem Bank 8.5. Find the tension in the cable if the coefficient of friction is (a) zero, and (b) 0.20.

8.6. A crate weighing 1250 N slides down an inclined plane at uniform speed. The plane is 6 m long and 3 m high. What is the coefficient of friction of the crate against the inclined plane? 8.7. A block of wood slides at constant speed down a 1 m plane when one end of the plane is raised to a height of 0.3 m. The mass of the block of wood is 5 kg. Find the coefficient of friction. 8.8. A 200 kg carton is to be moved up an inclined plane 4 m long and 3.1 m high. The coefficient of friction is 0.30. What force is necessary to move the carton at uniform speed up the plane? 8.9. Pat can push with a force of 120 N. What is the angle of the inclined plane that Pat should use to move a 600 N piano up her front stairs? Ignore friction. 8.10.A car runs out of gas while going 30 m/s up a 25° hill. If the brakes are not applied, how far up the incline will the car go before stopping? 8.11.A book slides down a 25° incline with an acceleration of 0.6 m/s2. Determine the coefficient of friction between the book and the incline. 8.12.A sled slides down a 35° incline with a constant acceleration. The sled starts at rest at the top and travels 15 m to the bottom, where its speed is 2.5 m/s. Find the coefficient of friction and the sled’s acceleration. 8.13.A counterweight of 4000 kg is used to pull a car along a 20° incline in a mine shaft, as shown below. (a) Find the acceleration of the car and the tension in the cable (b) Find the counterweight that would be needed in order for the car to move down the incline with an acceleration of 1.5 m/s2.
1800 kg 20°

4000 kg

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