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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. What mass of fuel is needed to reach a top speed of 4000 m/s?
A 250 g ball collides with a wall. FIGURE EX11.13 shows the ball€™s velocity and the force exerted on the ball by the wall. What is vfx, the ball€™s rebound velocity? F, (N) V,
A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in FIGURE EX11.9. What are the object€™s speed and direction after the force ends? F, (N)
A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in FIGURE EX11.8. What are the object€™s speed and direction after the force ends? F, (N)
A small rocket with 15 kN thrust burns 250 kg of fuel in 30 s. What is the exhaust speed of the hot gases?
At the center of a 50-m-diameter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds on to a 60 kg skater who had been heading west at 3.5 m/s.a. How long will it
A 20 g ball of clay traveling east at 3.0 m/s collides with a 30 g ball of clay traveling north at 2.0 m/s. What are the speed and the direction of the resulting 50 g ball of clay? Give your answer
An object at rest explodes into three fragments. FIGURE EX11.32 shows the momentum vectors of two of the fragments. What is the momentum of the third fragment? Write your answer using unit vectors.
Two particles collide and bounce apart. FIGURE EX11.31 shows the initial momenta of both and the final momentum of particle 2. What is the final momentum of particle 1? Write your answer using unit
A ball of mass m and another ball of mass 3m are placed inside a smooth metal tube with a massless spring compressed between them. When the spring is released, the heavier ball flies out of one end
Two ice skaters, with masses of 50 kg and 75 kg, are at the center of a 60-m-diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier
Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground?Dan’s mass is
A 70.0 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the player’s speed afterward if the ball is thrown ata. 15.0 m/s
A 50 kg archer, standing on frictionless ice, shoots a 100 g arrow at a speed of 100 m/s. What is the recoil speed of the archer?
package of mass m is released from rest at a warehouse loading dock and slides down the 3.0-m-high, frictionless chute of FIGURE EX11.25 to a waiting truck. Unfortunately, the truck driver went on a
A 50 g ball of clay traveling at speed v0 hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface.a. What is the speed of the brick after the collision?b. What percentage of the
A proton is traveling to the right at 2.0 × 107 m/s. It has a headon perfectly elastic collision with a carbon atom. The mass of the carbon atom is 12 times the mass of the proton. What are the
A 50 g marble moving at 2.0 m/s strikes a 20 g marble at rest. What is the speed of each marble immediately after the collision?
Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the
A 1500 kg car is rolling at 2.0 m/s. You would like to stop the car by firing a 10 kg blob of sticky clay at it. How fast should you fire the clay?
The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 1.0 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your
A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it at a speed of 30 m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the bird’s speed immediately
Three identical train cars, coupled together, are rolling east at speed v0. A fourth car traveling east at 2v0 catches up with the three and couples to make a four-car train. A moment later, the
A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the
A 10,000 kg railroad car is rolling at 2.0 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the car’s speed just after the gravel is loaded?
A 5000 kg open train car is rolling on frictionless rails at 22 m/s when it starts pouring rain. A few minutes later, the car’s speed is 20 m/s. What mass of water has collected in the car?
Two balls of clay of known masses hang from the ceiling on massless strings of equal length. They barely touch when both hang at rest. One ball is pulled back until its string is at 45°, then
A 600 g air-track glider collides with a spring at one end of the track. FIGURE EX11.12 shows the glider€™s velocity and the force exerted on the glider by the spring. How long is the
Two ice skaters, Paula and Ricardo, push off from each other. Ricardo weighs more than Paula.a. Which skater, if either, has the greater momentum after the push-off? Explain.b. Which skater, if
Far in space, where gravity is negligible, a 425 kg rocket traveling at 75 m/s fires its engines. FIGURE EX11.11 shows the thrust force as a function of time. The mass lost by the rocket during these
Two particles collide, one of which was initially moving and the other initially at rest.a. Is it possible for both particles to be at rest after the collision? Give an example in which this happens,
A sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.0 m/s and at point B is 5.0 m/s. Use the momentum principle to find how
Suppose a rubber ball collides head-on with a more massive steel ball traveling in the opposite direction with equal speed. Which ball, if either, receives the larger impulse? Explain.
A golf club continues forward after hitting the golf ball. Is momentum conserved in the collision? Explain, making sure you are careful to identify “the system.”
Automobiles are designed with “crumple zones” intended to collapse in a collision. Use the ideas of this chapter to explain why.
FIGURE EX11.7 is an incomplete momentum bar chart for a 50 g particle that experiences an impulse lasting 10 ms. What were the speed and direction of the particle before the impulse? kg m/s -2 -4- J.
It feels better to catch a hard ball while wearing a padded glove than to catch it bare handed. Use the ideas of this chapter to explain why.
FIGURE EX11.6 is an incomplete momentum bar chart for a collision that lasts 10 ms. What are the magnitude and direction of the average collision force exerted on the object? kg m/s 2 - 0- -2 - -4-
Angie, Brad, and Carlos are discussing a physics problem in which two identical bullets are fired with equal speeds at equal mass wood and steel blocks resting on a frictionless table. One bullet
In FIGURE EX11.5, what value of Fmaxgives an impulse of 6.0 N s? F, max 0+ 2 t (ms) 10 4 8. FIGURE EX11.5
A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a distance of 1 m, starting from rest. After
What is the impulse on a 3.0 kg particle that experiences the force shown in FIGURE EX11.4? F, (N) 2000 - 1500 1000 500 0+ 0 2 4 6 8 10 12 -t (ms) FIGURE EX11.4
A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a time of 1 s, starting from rest. After the
What impulse does the force shown in FIGURE EX11.3 exert on a 250 g particle? F, (N) 1000- -t (ms) 6. 0+ 2 4 FIGURE EX11.3
A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of -4 N s. What are the object’s speed and direction after the impulse?
What is the magnitude of the momentum ofa. A 3000 kg truck traveling at 15 m/s?b. A 200 g baseball thrown at 40 m/s?
A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of 4 N s. What are the object’s speed and direction after the impulse?
At what speed do a bicycle and its rider, with a combined mass of 100 kg, have the same momentum as a 1500 kg car traveling at 5.0 m/s?
Rank in order, from largest to smallest, the momenta (px)ato (px)eof the objects in FIGURE Q11.1. 20 g 20 g 200 g b 2 m/s 1 m/s 0.1 m/s 10 g 10 g 1 m/s 2 m/s FIGURE Q11.1
A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in FIGURE CP10.74. a. Find an expression for the sled??s speed when it is at angle ϕ.b. Use Newton??s
The spring in FIGURE CP10.73 has a spring constant of 1000 N/m. It is compressed 15 cm, then launches a 200 g block. The horizontal surface is frictionless, but the block€™s coefficient of
A 10 kg box slides 4.0 m down the frictionless ramp shown in FIGURE CP10.72, then collides with a spring whose spring constant is 250 N/m. a. What is the maximum compression of the spring?b. At what
It’s your birthday, and to celebrate you’re going to make your first bungee jump. You stand on a bridge 100 m above a raging river and attach a 30-m-long bungee cord to your harness. A bungee
In a physics lab experiment, a compressed spring launches a 20 g metal ball at a 30° angle. Compressing the spring 20 cm causes the ball to hit the floor 1.5 m below the point at which it leaves the
A pendulum is formed from a small ball of mass m on a string of length L. As FIGURE CP10.69 shows, a peg is height h = L/3 above the pendulum€™s lowest point. From what minimum angle
You are given the equation used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation.b. Draw the before-and-after pictorial
You are given the equation used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation.b. Draw the before-and-after pictorial
You are given the equation used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation.b. Draw the before-and-after pictorial
Write a realistic problem for which the energy bar chart shown in FIGURE P10.65 correctly shows the energy at the beginning and end of the problem. E (J) 40 20 -20 - K; + UGi+ Uspi = K¡ + Ugf+Uspf
An object moving in the xy-plane is subjected to the force Fu = (2xy î + 3y ĵ) N, where x and y are in m.a. The particle moves from the origin to the point with coordinates (a, b) by moving first
An object moving in the xy-plane is subjected to the force F = (2xy î + x2 ĵ) N, where x and y are in m.a. The particle moves from the origin to the point with coordinates (a, b) by moving
A particle that can move along the x-axis experiences an interaction force Fx = (3x2 - 5x) N, where x is in m. Find an expression for the system’s potential energy.
The potential energy for a particle that can move along the x-axis is U = Ax2 + B sin(πx/L), where A, B, and L are constants. What is the force on the particle at(a) x = 0,(b) x = L/2,(c) x = L?
A clever engineer designs a “sprong” that obeys the force law Fx = -q(x - xeq)3, where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity,
A 100 g particle experiences the one-dimensional, conservative force Fxshown in FIGURE P10.59.a. Let the zero of potential energy be at x = 0 m. What is the potential energy at x = 1.0, 2.0, 3.0, and
A particle that can move along the x-axis is part of a system with potential energywhere A and B are positive constants.a. Where are the particle€™s equilibrium positions?b. For each, is it
A system has potential energy U(x) = x + sin((2 rad/m)x) as a particle moves over the range 0 m ≤ x ≤ π m.a. Where are the equilibrium positions in this range?b. For each, is it a point of
A 2.6 kg block is attached to a horizontal rope that exerts a variable force Fx = (20 - 5x) N, where x is in m. The coefficient of kinetic friction between the block and the floor is 0.25. Initially
Protons and neutrons (together called nucleons) are held together in the nucleus of an atom by a force called the strong force. At very small separations, the strong force between two nucleons is
The spring shown in FIGURE P10.54 is compressed 50 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student??s coefficient of kinetic
a. A 50 g ice cube can slide without friction up and down a 30° slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25
Use work and energy to find an expression for the speed of the block in FIGURE P10.52 just before it hits the floor if (a) The coefficient of kinetic friction for the block on the table is μk (b)
A freight company uses a compressed spring to shoot 2.0 kg packages up a 1.0-m-high frictionless ramp into a truck, as FIGURE P10.51 shows. The spring constant is 500 N/m and the spring is compressed
Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward
A horizontal spring with spring constant 100 N/m is compressed 20 cm and used to launch a 2.5 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface
Sam, whose mass is 75 kg, straps on his skis and starts down a 50-m-high, 20° frictionless slope. A strong headwind exerts a horizontal force of 200 N on him as he skies. Use work and energy to find
You have a ball of unknown mass, a spring with spring constant 950 N/m, and a meter stick. You use various compressions of the spring to launch the ball vertically, then use the meter stick to
A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?
A block of mass m slides down a frictionless track, then around the inside of a circular loop-the-loop of radius R. From what minimum height h must the block start to make it around without falling
It€™s been a great day of new, frictionless snow. Julie starts at the top of the 60° slope shown in FIGURE P10.44. At the bottom, a circular arc carries her through a 90 turn, and she
You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 10-m-high hill, then descends 15 m to the track’s lowest point. You’ve
A 50 g ice cube can slide up and down a frictionless 30° slope. At the bottom, a spring with spring constant 25 N/m is compressed 10 cm and used to launch the ice cube up the slope. How high
A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The ice cube’s speed at the bottom of the circle is 3.0 m/s. What is the ice
A cable with 20.0 N of tension pulls straight up on a 1.50 kg block that is initially at rest. What is the block’s speed after being lifted 2.00 m? Solve this problem using work and energy.
How much work is done by the environment in the process shown in FIGURE EX10.39? Is energy transferred from the environment to the system or from the system to the environment? E (J) 1,2.1 01 K; + U
What is the final kinetic energy of the system for the process shown in FIGURE EX10.38? E (J) 4 3 K; + U; + Wext = K; + U; + AE FIGURE EX10.38
A system loses 400 J of potential energy. In the process, it does 400 J of work on the environment and the thermal energy increases by 100 J. Show this process on an energy bar chart.
A force does work on a 50 g particle as the particle moves along the following straight paths in the xy-plane: 25 J from (0 m, 0 m) to (5 m, 0 m); 35 J from (0 m, 0 m) to (0 m, 5 m); –5 J from (5
A particle moves from A to D in FIGURE EX10.35 while experiencing force F = (6iÌ‚ + 8jÌ‚) N. How much work does the force do if the particle follows path(a) ABD,(b)
FIGURE EX10.34 shows the potential energy of a system in which a particle moves along the x-axis. Draw a graph of the force Fxas a function of position x. U (J) 2- 04 FIGURE EX10.34
A particle moving along the x-axis is in a system with potential energy U = 10/x J, where x is in m. What is the x-component of the force on the particle at x = 2 m, 5 m, and 8 m?
A particle moving along the y-axis is in a system with potential energy U = 4y3 J, where y is in m. What is the y-component of the force on the particle at y = 0 m, 1 m, and 2 m?
A system in which only one particle can move has the potential energy shown in FIGURE EX10.31. What is the y component of the force on the particle at y = 0.5 m and 4 m? U (J) 60 ry (m) 5 0- 2 FIGURE
A system in which only one particle can move has the potential energy shown in FIGURE EX10.30. What is the x component of the force on the particle at x = 5, 15, and 25 cm? U (J) 10- 0+ -x (cm) 40 T
In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m? U (J) 16- 12 - 8- 4. 0+ x (m) FIGURE EX10.28 4 2.
FIGURE EX10.28 shows the potential energy of a 500 g particle as it moves along the x-axis. Suppose the particle??s mechanical energy is 12 J. a. Where are the particle??s turning points?b. What is
a. In FIGURE EX10.27, what minimum speed does a 100 g particle need at point A to reach point B?b. What minimum speed does a 100 g particle need at point B to reach point A? U (J) 5- 2- 0+ B FIGURE
In FIGURE EX10.26, what is the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm? U (J) 5- 4 3- 2- 0+ x (mm) 4 FIGURE EX10.26
FIGURE EX10.25 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particle€™s speeds at B, C, and D? U (J) 5- 4 3 2- 0+ B D FIGURE EX10.25
FIGURE EX10.24 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0 m.a. Will the particle move to the right or to the left?b. What is the particle€™s

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