The diagram below shows a block of mass m=2.00kgđ=2.00kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F1=4.00Nđš1=4.00N, F2=6.00Nđš2=6.00N, and F3=8.00Nđš3=8.00N are applied to the block, initially at rest on the surface, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive).Figure1 of 1Part APart completeCalculate the magnitude of the total resultant force Fâ r=Fâ 1+Fâ 2+Fâ 3đšâr=đšâ1+đšâ2+đšâ3 acting on the mass.Express your answer in Newtons to three significant figures.View Available Hint(s)for Part A|Fâ r||đšâr| =1.83NNSubmitPrevious AnswersAnswer RequestedPart BPart completeWhat angle does Fâ rđšâr make with the positive x axis?Express your answer in degrees to two significant figures.View Available Hint(s)for Part B-73degreesSubmitPrevious AnswersAll attempts used; correct answer displayedPart CPart completeWhat is the magnitude of the mass's acceleration vector, aâ đâ?Express your answer to two significant figures.View Available Hint(s)for Part C|aâ ||đâ| =0.92m/s2m/s2SubmitPrevious AnswersAll attempts used; correct answer displayedPart DPart completeWhat is the direction of aâ đâ? In other words, what angle does this vector make with respect to the positive x axis?Express your answer in degrees to two significant figures.View Available Hint(s)for Part D-73degreesSubmitPrevious AnswersAll attempts used; correct answer displayedPart EHow far (in meters) will the mass move in 5.0 s?Express the distance dđ in meters to two significant figures.View Available Hint(s)for Part EActivate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typedđ =mmSubmitPrevious Answers Incorrect; Try Again; 9 attempts remainingPart FWhat is the magnitude of the velocity vector of the block at t=5.0sđĄ=5.0s?Express your answer in meters per second to two significant figures.View Available Hint(s)for Part FActivate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type|vâ (5)||đŁâ(5)| =m/sm/sSubmitPrevious Answers Incorrect; Try Again; 9 attempts remainingPart GIn what direction is the mass moving at time t=5.0sđĄ=5.0s? That is, what angle does the velocity vector make with respect to the positive x axis?Express your answer in degrees to two significant figures.View Available Hint(s)
Question
The diagram below shows a block of mass m=2.00kgđ=2.00kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F1=4.00Nđš1=4.00N, F2=6.00Nđš2=6.00N, and F3=8.00Nđš3=8.00N are applied to the block, initially at rest on the surface, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive).Figure1 of 1Part APart completeCalculate the magnitude of the total resultant force Fâ r=Fâ 1+Fâ 2+Fâ 3đšâr=đšâ1+đšâ2+đšâ3 acting on the mass.Express your answer in Newtons to three significant figures.View Available Hint(s)for Part A|Fâ r||đšâr| =1.83NNSubmitPrevious AnswersAnswer RequestedPart BPart completeWhat angle does Fâ rđšâr make with the positive x axis?Express your answer in degrees to two significant figures.View Available Hint(s)for Part B-73degreesSubmitPrevious AnswersAll attempts used; correct answer displayedPart CPart completeWhat is the magnitude of the mass's acceleration vector, aâ đâ?Express your answer to two significant figures.View Available Hint(s)for Part C|aâ ||đâ| =0.92m/s2m/s2SubmitPrevious AnswersAll attempts used; correct answer displayedPart DPart completeWhat is the direction of aâ đâ? In other words, what angle does this vector make with respect to the positive x axis?Express your answer in degrees to two significant figures.View Available Hint(s)for Part D-73degreesSubmitPrevious AnswersAll attempts used; correct answer displayedPart EHow far (in meters) will the mass move in 5.0 s?Express the distance dđ in meters to two significant figures.View Available Hint(s)for Part EActivate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typedđ =mmSubmitPrevious Answers Incorrect; Try Again; 9 attempts remainingPart FWhat is the magnitude of the velocity vector of the block at t=5.0sđĄ=5.0s?Express your answer in meters per second to two significant figures.View Available Hint(s)for Part FActivate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type|vâ (5)||đŁâ(5)| =m/sm/sSubmitPrevious Answers Incorrect; Try Again; 9 attempts remainingPart GIn what direction is the mass moving at time t=5.0sđĄ=5.0s? That is, what angle does the velocity vector make with respect to the positive x axis?Express your answer in degrees to two significant figures.View Available Hint(s)
Solution
I'm sorry, but your question is not clear. Could you please provide the diagram or more details about the angles at which the forces are applied? This information is crucial to solve the problem.
However, I can guide you on how to approach this problem:
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First, you need to resolve each force into its x and y components. The x-component of a force is given by Fcos(θ) and the y-component is given by Fsin(θ), where F is the magnitude of the force and θ is the angle it makes with the x-axis.
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Once you have the components, you can add them up to get the total force in the x and y direction. The total force in the x direction (Fx) is the sum of the x-components of all the forces, and the total force in the y direction (Fy) is the sum of the y-components of all the forces.
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The magnitude of the resultant force (Fr) can be found using the Pythagorean theorem: Fr = sqrt(Fx^2 + Fy^2).
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The angle θr that the resultant force makes with the x-axis can be found using the arctangent function: θr = atan(Fy/Fx). Make sure to adjust the angle depending on the quadrant.
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The acceleration of the block can be found using Newton's second law: a = Fr/m, where m is the mass of the block.
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The direction of the acceleration is the same as the direction of the resultant force.
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The distance the block moves in a given time can be found using the equation of motion: d = 0.5at^2, where t is the time.
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The velocity of the block at a given time can be found using the equation v = a*t.
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The direction of the velocity is the same as the direction of the acceleration.
Please provide the angles at which the forces are applied so I can help you solve this problem.
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