Mastering Physics Solutions: Kirchhoff’s Rules and Applying Them

Mastering Physics Solutions: Kirchhoff’s Rules and Applying Them

On September 23, 2013, in Chapter 18: Basic Electric Circuits, by Mastering Physics Solutions

Part A = current
Part B = I2 + I3 – I1
Part C = I3 ⋅ R3 – I2 ⋅ R2
Part D = Vb – I1 ⋅ R1 – I3 ⋅ R3

The junction rule describes the conservation of which quantity? Note that this rule applies only to circuits that are in a steady state.
Apply the junction rule to the junction labeled with the number 1 (at the bottom of the resistor of resistance R2).
Apply the loop rule to loop 2 (the smaller loop on the right). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow. Remember that the current meter is ideal.
Now apply the loop rule to loop 1 (the larger loop spanning the entire circuit). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow.

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Mastering Physics Solutions: A Gymnast on a Rope

Mastering Physics Solutions: A Gymnast on a Rope

On September 22, 2013, in Chapter 04: Force and Motion, by Mastering Physics Solutions

Part A = 491 N Click to use the calculator/solver for this part of the problem
Part B = 491 N Click to use the calculator/solver for this part of the problem
Part C = 556 N Click to use the calculator/solver for this part of the problem
Part D = 426 N Click to use the calculator/solver for this part of the problem

Calculate the tension T in the rope if the gymnast hangs motionless on the rope.
Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.
Calculate the tension T in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.30 m/s2.
Calculate the tension T in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.30 m/s2.

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Mastering Physics Solutions: Motion of a Block with Three Forces

Mastering Physics Solutions: Motion of a Block with Three Forces

On September 21, 2013, in Chapter 04: Force and Motion, by Mastering Physics Solutions

Part A = 1.83 N Click to use the calculator/solver for this part of the problem
Part B = -73° Click to use the calculator/solver for this part of the problem
Part C = 0.92 m/s2 Click to use the calculator/solver for this part of the problem
Part D = -73° Click to use the calculator/solver for this part of the problem
Part E = 11 m Click to use the calculator/solver for this part of the problem
Part F = 4.6 m/s Click to use the calculator/solver for this part of the problem
Part G = -73° Click to use the calculator/solver for this part of the problem

Calculate the magnitude of the total resultant force Fr = F1 + F2 + F3 acting on the mass.
What angle does Fr make with the positive x axis?
What is the magnitude of the mass’s acceleration vector, a?
What is the direction of A? In other words, what angle does this vector make with respect to the positive x axis?
How far (in meters) will the mass move in 5.0 s?
What is the magnitude of the velocity vector of the block at t = 5.0 s?
In what direction is the mass moving at time t = 5.0 s? That is, what angle does the velocity vector make with respect to the positive x axis?

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Mastering Physics Solutions: Arrow Hits Apple

Mastering Physics Solutions: Arrow Hits Apple

On September 17, 2013, in Chapter 03: Motion in Two Dimensions, by Mastering Physics Solutions

Part A = 6.70 s
Part B = 5.59 s

Find the time that the arrow spends in the air.
Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree. How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree?

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Mastering Physics Solutions: A Canoe on a River

Mastering Physics Solutions: A Canoe on a River

On September 17, 2013, in Chapter 03: Motion in Two Dimensions, by Mastering Physics Solutions

Part A = 0.4018 m/s
Part B = 75.43 °

Find the magnitude of the velocity of the canoe relative to the river.
Find the direction of the velocity of the canoe relative to the river.

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Mastering Physics Solutions: Speed of a Softball

Mastering Physics Solutions: Speed of a Softball

On September 16, 2013, in Chapter 03: Motion in Two Dimensions, by Mastering Physics Solutions

Part A = 18.77 m/s
Part B = 31.50 °
Part C = 16.0, -8.82 m/s

Find v0. Use g = 9.807 m/s2 for the magnitude of the acceleration due to gravity.
Find the angle in degrees.
Find a vector expression for the velocity v of the softball 0.1 s before the ball is caught.
Find a vector expression for the position r of the softball 0.1 s before the ball is caught.

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