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Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the bottom of slide 1 compare with v2, the speed of a swimmer reaching the end of slide 2 ? Slide 1 v1 > v2 v1 = v2 v1 < v2 The heavier swimmer will have a greater speed than the lighter swimmer, no matter which slide he uses. No simple relationship exists between v1 and v2.

Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the bottom of slide 1 compare with v2, the speed of a swimmer reaching the end of slide 2 ? Slide 1 v1 > v2 v1 = v2 v1 < v2 The heavier swimmer will have a greater speed than the lighter swimmer, no matter which slide he uses. No simple relationship exists between v1 and v2.

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Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h , slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v 1 of a swimmer reaching the bottom of slide 1 compare with v 2 , the speed of a swimmer reaching the end of slide 2 ? Slide 1 v 1 > v 2 v 1 = v 2 v 1 < v 2 The heavier swimmer will have a greater speed than the lighter swimmer, no matter which slide he uses. No simple relationship exists between v 1 and v 2 .

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Swimmers at a water park have a choice of two frictionless water slides as shown in the figure. Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide 1 compares with v2, the speed of a swimmer reaching the end of slide 2? (A) v1 > v2 (B) v1 < v2 (C) v1 = v2 (D) No simple relationship exists between v1 and v2 because we do not know the curvature of slide 2.
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Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.
Solution
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A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh. A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh. A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh. A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh. A load of bricks with mass m1 = 17.0 kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m2 = 31.0 kg is suspended from the other end of the rope, as shown in (Figure 1). The system is released from rest. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Two bodies with the same magnitude of acceleration. Part A Draw a free-body diagram for the load of bricks. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of the vectors will not be graded. No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Part C What is the magnitude of the upward acceleration of the load of bricks? Express your answer with the appropriate units. Part D What is the tension in the rope while the load is moving? Express your answer with the appropriate units. Part E How does the tension compare to the weight of the load of bricks? To the weight of the counterweight? Drag the terms on the left to the appropriate blanks on the right to complete the sentence. Reset Help smaller than The tension in the rope is the greater than weight of the load of bricks and the weight of the counterweigh.

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