Question

You are a member of an alpine rescue team and must get a box of supplies, with mass 2.60 kg , up an incline of constant slope angle 30.0 ° so that it reaches a stranded skier who is a vertical distance 2.70 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10?2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s² . Part A Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier. Express your answer numerically, in meters per second.

          You are a member of an alpine rescue team and must get a box of supplies, with mass 2.60 kg , up an incline of constant slope angle 30.0 ° so that it reaches a stranded skier who is a vertical distance 2.70 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10?2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s² .

Part A

Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier.

Express your answer numerically, in meters per second.

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You are a member of an alpine rescue team and must get a box of supplies, with mass 2.60 kg , up an incline of constant slope angle 30.0 ° so that it reaches a stranded skier who is a vertical distance 2.70 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10?2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s² .

Part A

Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier.

Express your answer numerically, in meters per second.

Added by Julia W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Mahnoor Khan

03/15/2022

Step 1

The normal force (N) can be calculated using the formula: \[ N = mg \cos(\alpha) \] where: m = mass of the box = 60 kg g = acceleration due to gravity = 9.81 m/s² α = angle of the slope = 30° \[ N = 60 \times 9.81 \times \cos(30°) \] \[ N = 60 \times 9.81 \times Show more…

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You are a member of an alpine rescue team and must get a box of supplies, with mass 2.60 kg , up an incline of constant slope angle 30.0 ° so that it reaches a stranded skier who is a vertical distance 2.70 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10−2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s² . Part A Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier. Express your answer numerically, in meters per second.

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Transcript

00:01 So let's start with the given data that we have for this question.

00:04 Now, the first thing that we have been given is the mass of the box of supplies, right? and that is equal to 2 .60 kilograms, right? then they have told us that there is a constant slope, right? constant slope and the angle of this slope, that is alpha, and it's equal to 30 degree.

00:28 Right? then they have told us the vertical distance that is basically the height right at which this person is standing and that is equal to 2 .70 meter right then they have told us that friction is present right and since fraction is present so it means that there must be some coefficient of kinetic fraction right and that is mu and it's equal to 6 .00 into 10 raised to power negative 2 right and then they have told us that we need to use the gravitation acceleration value that is equal to 9 .81 meter per second square right now what we need to find here is the initial sorry not the initial velocity but the velocity that is basically required right so yes in a sense you can say that it's initial velocity right so we need to find this velocity.

01:31 I mean, you find it using the work energy theorem, right? now, this question is very, very simple.

01:38 You have been given a bunch of information, and we are just going to use this information in order to solve our question.

01:44 Right.

01:46 Now, what we are going to do over here is very simple.

01:53 Fine.

01:54 The first thing that we are going to do over here, so we need to look at this a free body diagram, right, because that is very, very important for us over here, right, in order to solve this question...

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