CH 6 Physics Review Problems

A 40-kg box is being pushed along a horizontal smooth surface. The pushing force is 15 N directed at an angle of 15° below the horizontal. What is the magnitude of the acceleration of the crate?

0.36 m/s2

A 50.0-kg block is being pulled up a 16.0° slope by a force of 250 N that is parallel to the slope. The coefficient of kinetic friction between the block and the slope is 0.200. What is the acceleration of the block?

0.412 m/s2

A 200-N sled of slides down a frictionless hillside that rises at 37° above the horizontal. What is the magnitude of the force that the hill exerts on the sled parallel to the surface of the hill?

0 N

An ornament of mass 40.0 g is attached to a vertical ideal spring with a force constant (spring constant) of 20.0 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?

0.0196 m

During a hockey game, a puck is given an initial speed of 10 m/s. It slides 50 m on the horizontal ice before it stops due to friction. What is the coefficient of kinetic friction between the puck and the ice?

0.10

A horizontal 52-N force is needed to slide a 50-kg box across a flat surface at a constant velocity of 3.5 m/s. What is the coefficient of kinetic friction between the box and the floor?

0.11

A 50.0-kg crate is being pulled along a horizontal smooth surface. The pulling force is 10.0 N and is directed 20.0° above the horizontal. What is the magnitude of the acceleration of the crate?

0.188 m/s2

An object slides on a level floor. It slows and comes to a stop with a constant acceleration of magnitude 2.4 m/s2. What is the coefficient of kinetic friction between the object and the floor?

0.24

In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When block B is gently released from rest, how long does it take block B to travel 80.0 cm?

0.639 s

A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle is measured to be 18°, what is the speed of the mass?

1.1 m/s

Two forces act on a 55-kg object. One force has magnitude 65 N directed 59° clockwise from the positive x-axis, and the other has a magnitude 35 N at 32° clockwise from the positive y-axis. What is the magnitude of this object's acceleration?

1.1 m/s2

A 250-kg motorcycle goes around an unbanked turn of radius 13.7 m at a steady 96.5 km/h. What is the magnitude of the net force on the motorcycle?

1.31 x 10^4 N

A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can be reduced or even eliminated. How long should each rotation take for a doughnut-shaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of Earth?

1.5 min

A race car traveling at a constant speed of 50 m/s drives around a circular track that is 500 m in diameter. What is the magnitude of the acceleration of the car?

10 m/s2

A 2.0-kg ball is moving with a constant speed of 5.0 m/s in a horizontal circle whose diameter is 1.0 m. What is the magnitude of the net force on the ball?

100N

Two blocks, A and B, are being pulled to the right along a horizontal surface by a horizontal 100-N pull, as shown in the figure. Both of them are moving together at a constant velocity of 2.0 m/s to the right, and both weigh the same. Which of the figures below shows a correct free-body diagram of the horizontal forces acting on the lower block, B?

100N pulling each way horizontally

A particularly scary roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 13.2 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.

11.4 m/s

A 3.0-kg and a 5.0-kg box rest side-by-side on a smooth, level floor. A horizontal force of 32 N is applied to the 5.0-kg box pushing it against the 3.0-kg box, and, as a result, both boxes slide along the floor. How hard do the two boxes push against each other?

12 N

The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the speedway banked?

32°

A policeman investigating an accident measures the skid marks left by a car on the horizontal road. He determines that the distance between the point that the driver slammed on the brakes (thereby locking the wheels) and the point where the car came to a stop was 28.0 m. From a reference manual he determines that the coefficient of kinetic friction between the tires and the road under the prevailing conditions was 0.300. How fast was the car going when the driver applied the brakes?

12.8 m/s

A 3.0-kg brick rests on a perfectly smooth ramp inclined at 34° above the horizontal. The brick is kept from sliding down the plane by an ideal spring that is aligned with the surface and attached to a wall above the brick. The spring has a spring constant (force constant) of 120 N/m. By how much does the spring stretch with the brick attached?

14 cm

A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30. A horizontal 140-N force is applied to the box. What is the friction force on the box?

140 N

A load is being lifted vertically upwards by means of two cables attached to it. The first cable exerts a force of 600 N at an angle of 35.0° to the left of the vertical. The second cable exerts a force of 1300 N. At what angle to the right of the vertical is the second cable pulling?

15.4°

The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes 0.53 s for it to reach the floor. What is the mass m of the block on the left? There is no friction or mass in the pulley, and the connecting rope is very light.

16 kg

A 200-N sled of slides down a frictionless hillside that rises at 37° above the horizontal. What is the magnitude of the force that the surface of the hill exerts on the sled?

160 N

In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top of a vertical circle with a radius of 2.5 km?

160 m/s

Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle. At the bottom of the dive, the speed of the airplane is 320 m/s. What is the smallest radius allowable for the vertical circle if the pilot's apparent weight is not to exceed 7.0 times his true weight?

1700m

A 1000-kg barge is being towed by means of two horizontal cables. One cable is pulling with a force of 80.0 N in a direction 30.0° west of north. In what direction should the second cable pull so that the barge will accelerate northward, if the force exerted by the cable is 120 N? Assume that the water exerts no appreciable frictional drag on the barge.

19.5° east of north

A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.35. At what speed will the car begin to skid sideways?

19m/s

The figure shows a block of mass m resting on a 20° slope. The block has coefficients of friction

2.1kg

A 3.0-kg mass and a 5.0-kg mass hang vertically at the opposite ends of a very light rope that goes over an ideal pulley. If the masses are gently released, what is the resulting acceleration of the masses?

2.5 m/s2

A baseball player is running to second base at 5.03 m/s. When he is 4.80 m from the plate he goes into a slide. The coefficient of kinetic friction between the player and the ground is 0.180, and the coefficient of static friction is 3.14. What is his speed when he reaches the plate?

2.89 m/s

A 3.0-kg and a 5.0-kg box rest side-by-side on a perfectly smooth, level floor. A horizontal force of 32 N is applied to the 3.0-kg box pushing it against the 5.0-kg box, and, as a result, both boxes slide along the floor. How hard do the two boxes push against each other?

20 N

A point on a wheel of radius 40 cm that is rotating at a constant 5.0 revolutions per second is located 0.20 m from the axis of rotation. What is the acceleration of that point due to the spin of the wheel?

200 m/s2

A flatbed truck is carrying a 20-kg crate up a sloping road. The coefficient of static friction between the crate and the bed is 0.40, and the coefficient of kinetic friction is 0.30. What is the maximum angle of slope that the truck can climb at constant speed if the crate is to stay in place?

22 degrees

A 50-kg box is resting on a horizontal floor. A force of 250 N directed at an angle of 30.0° below the horizontal is applied to the box. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.30. What is the force of friction on the box?

220 N

A 50-kg box is being pushed along a horizontal surface. The coefficient of static friction between the box and the ground is 0.65, and the coefficient of kinetic friction is 0.35. What horizontal force must be exerted on the box for it to accelerate at 1.2 m/s2?

230 N

A 400-kg box is lifted vertically upward with constant velocity by means of two cables pulling at 40.0° on either side of the vertical direction. What is the tension in each cable?

2560 N

Three boxes rest side-by-side on a smooth, horizontal floor. Their masses are 5.0 kg, 3.0kg, and 2.0 kg, with the 3.0-kg mass in the center. A force of 50 N pushes on the 5.0-kg box, which pushes against the other two boxes. What magnitude force does the 5.0-kg box exert on the 3.0-kg box?

25N

A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand without breaking is 350 N. What is the maximum speed the mass can have without breaking the string?

26 m/s

A 6.00-kg ornament is held at rest by two light wires that form 30° angles with the vertical, as shown in the figure. An external force of magnitude F acts vertically downward on the ornament. The tension exerted by each of the two wires is denoted by T. A free-body diagram, showing the four forces that act on the box, is shown in the figure. If the magnitude of force F is 410 N, what is the magnitude of the tension T?

271 N

A highway curve of radius 80 m is banked at 45°. Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road?

28 m/s

One way that future space stations may create artificial gravity is by rotating the station. Consider a cylindrical space station 380 m in diameter that is rotating about its longitudinal axis. Astronauts walk on the inside surface of the space station. How long will it take for each rotation of the cylinder if it is to provide "normal" gravity for the astronauts?

28 s

A very light ideal spring stretches by 21.0 cm when it is used to hang a 135-N object. What is the weight of a piece of electronic equipment that would stretch the spring by 44.9 cm if you hung the equipment using the spring?

289 N

An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant) of the spring is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at 1.4 m/s2, what is the mass of the object?

28kg

A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

29.1°

A 6.0-kg box slides down an inclined plane that makes an angle of 39° with the horizontal. If the coefficient of kinetic friction is 0.40, at what rate does the box accelerate down the slope?

3.1 m/s2

A flatbed truck is carrying a 20.0-kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.400, and the coefficient of kinetic friction is 0.300. What is the maximum acceleration that the truck can have if the crate is to stay in place relative to the truck?

3.92 m/s2

A highway curve of radius 100 m, banked at an angle of 45°, may be negotiated without friction at a speed of

31 m/s

You are driving at 30.0 m/s on a freeway curve of radius 25.0 m. What is the magnitude of your acceleration?

36.0 m/s2

A driver in a 1000-kg car traveling at 24 m/s slams on the brakes and skids to a stop. If the coefficient of friction between the tires and the level road is 0.80, how long will the skid marks be?

37 m

Jason takes off across level water on his jet-powered skis. The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible). The skis produce a forward thrust of 200 N and have a coefficient of kinetic friction with water of 0.10. Unfortunately, the skis run out of fuel after only 41 s. How far from his starting point has Jason traveled when he finally coasts to a stop?

3900 m

A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. The car maintains its speed over the bump. What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the top of the bump?

390N

A 15-kg block is on a frictionless ramp that is inclined at 20° above the horizontal. It is connected by a very light string over an ideal pulley at the top edge of the ramp to a hanging 19-kg block, as shown in the figure. The string pulls on the 15-kg block parallel to the surface of the ramp. Find the magnitude of the acceleration of the 19-kg block after the system is gently released?

4.0 m/s2

In a shuffleboard game, the puck slides a total of 12 m on a horizontal surface before coming to rest. If the coefficient of kinetic friction between the puck and board is 0.10, what was the initial speed of the puck?

4.8 m/s

A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second unbanked curve of radius 320 m if the coefficient of static friction between the car's tires and the road surface is the same in both cases?

40 m/s

A force of 30 N stretches a very light ideal spring 0.73 m from equilibrium. What is the force constant (spring constant) of the spring?

41 N/m

A piano mover raises a 1000-N piano at a constant speed using a very light rope in a frictionless pulley system, as shown in the figure. With what force is the mover pulling down on the rope?

500 N

The figure shows a block of mass M hanging at rest. The light wire fastened to the wall is horizontal and has a tension of 38 N. The wire fastened to the ceiling is also very light, has a tension of 59 N, and makes an angle

50°

What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding?

51°

The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is 0.40, what would be the maximum safe driving speed for this horizontal curved section of highway?

54 m/s

An object moves with a constant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object?

6.0 m/s2

A 10.0-kg picture is held in place by two wires, the first one hanging at 50.0° to the left of the vertical and the second one at 45.0° to the right of the vertical. What is the tension in the first wire?

69.6 N

A 200-g hockey puck is launched at an initial speed of 16 m/s up a metal ramp that is inclined at a 30° angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are μs = 0.40 and μk = 0.30, respectively. What vertical height does the puck reach above its starting point?

8.6 cm

The coefficients of static and kinetic friction between a 3.0-kg box and a horizontal desktop are 0.40 and 0.30, respectively. What is the force of friction on the box when a 15-N horizontal push is applied to the box?

8.8 N

In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against the wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the passengers can have so they do not fall if the coefficient of static friction between the passengers and the wall is 0.25?

8.9 m/s

You push downward on a trunk at an angle 25° below the horizontal with a force of 750 N. If the trunk is on a flat surface and the coefficient of static friction between the surface and the trunk is 0.61, what is the most massive trunk you will be able to move?

81 kg

A tightrope walker walks across a 30-m long wire tied between two poles. The center of the wire is displaced vertically downward by 1.0 m when he is halfway across. If the tension in both halves of the wire at this point is 6294 N, what is the mass of the tightrope walker? Neglect the mass of the wire.

85 kg

A 10-kg sign is held by two ropes as shown in the figure. What is the tension on rope A?

88 N

A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of the circular section of a dive. What is the radius of curvature of this section of the dive?

9.2 km

A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding?

9000 N

A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of a circular dive. What is the radius of curvature of the circular part of the path in which the plane is flying?

9200 m

An object is being acted upon by three forces and as a result moves with a constant velocity. One force is 60.0 N along the +x-axis, and the second is 75.0 N along the +y-axis. What is the magnitude of the third force?

96.0 N

A block of mass m sits at rest on a rough inclined ramp that makes an angle

F = mg cos

If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens because an outward force balances the pull of gravity on the water.

False

The Moon is accelerated toward the earth, so it is gradually getting closer to the earth.

False

Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely to slide on the pavement as it goes around the curve?

Neither car will slide.

Two blocks, A and B, are being pulled to the right along a horizontal surface by a horizontal 100-N pull, as shown in the figure. Both of them are moving together at a constant velocity of 2.0 m/s to the right, and both weigh the same. Which of the figures below shows a correct free-body diagram of the horizontal forces acting on the upper block, A?

No horizontal forces act on A

In the figure, a 10-lb weight is suspended from two spring scales, each of which has negligible weight. Which one of the following statements about the readings in the scales is true?

None of these are true

As shown in the figure, a woman is straining to lift a large crate, but without success because it is too heavy. We denote the forces on the crate as follows: P is the magnitude of the upward force being exerted on the crate by the person, C is the magnitude of the vertical contact force on the crate by the floor, and W is the weight of the crate. How are the magnitudes of these forces related while the person is trying unsuccessfully to lift the crate?

P + C = W

A push of magnitude P acts on a box of weight W as shown in the figure. The push is directed at an angle

P cos 0

Two boxes are connected to each other by a string as shown in the figure. The 10-N box slides without friction on the horizontal table surface. The pulley is ideal and the string has negligible mass. What is true about the tension T in the string?

T < 30 N

Three boxes are pulled along a horizontal frictionless floor by a constant horizontal pull P. The boxes are connected by very light horizontal strings having tensions T1 and T2 as shown in the figure. Which of the following statements about the tensions is correct?

T1 > T2

Two objects have masses m and 5m, respectively. They both are placed side by side on a frictionless inclined ramp and allowed to slide down from rest without any air resistance. Which one of the following statements about these objects is correct?

The two objects reach the bottom of the ramp at exactly the same time.

An object moves in a circular path at a constant speed. Compare the direction of the object's velocity and acceleration vectors.

The vectors are perpendicular to each other.

A push of magnitude P acts on a box of weight W as shown in the figure. The push is directed at an angle

W + P sin

When an object moves in uniform circular motion, the direction of its acceleration is

directed toward the center of its circular path

In the figure, what does the spring scale read? The pulleys are ideal and the strings and scale are also massless.

exactly 1.0 N

If a satellite moves with constant speed in a perfectly circular orbit around the earth, what is the direction of the acceleration of the satellite?

inward toward the earth

You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the ice, it

moves along a straight-line path in its original direction.

A car goes around a circular curve on a horizontal road at constant speed. What is the direction of the friction force on the car due to the road?

perpendicular to the curve inward

When a car goes around a circular curve on a horizontal road at constant speed, what force causes it to follow the circular path?

the friction force from the road

Two boxes, A and B, are connected by a horizontal string S on a horizontal floor. A very light wire pulls horizontally on box B, as shown in the figure, with a force of 100 N. The reaction force to this pull is

the pull of box B on the wire