A 60° inclined plane of length 0.30 m is positioned at the edge of a table that is 1.0 m high, as shown in (Figure 1). A box is placed at the top of the plane and given a shove so that it has an initial velocity of 2.0 m/s down the plane. The coefficient of kinetic friction between the block and the plane is μ=0.80. (a) Calculate the speed of the block when it reaches the bottom of the plane. (b) Find the speed of the block when it is 0.90 m above the floor. (c) Is the total mechanical energy of the block conserved as it moves from the top of the plane to the floor? Figure 1.0 m < -0.30 m 60% 1 of 1 >

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Chapter1: Units, Trigonometry. And Vectors
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Review | Constants
A 60° inclined plane of length 0.30 m is positioned at the
edge of a table that is 1.0 m high, as shown in (Figure 1).
A box is placed at the top of the plane and given a shove
so that it has an initial velocity of 2.0 m/s down the
plane. The coefficient of kinetic friction between the block
and the plane is μk = 0.80. (a) Calculate the speed of the
block when it reaches the bottom of the plane. (b) Find
the speed of the block when it is 0.90 m above the floor.
(c) Is the total mechanical energy of the block conserved
as it moves from the top of the plane to the floor?
Write an expression for the sum of kinetic and potential energies of the box at the initial moment.
Throughout the problem, we denote the mass of the box as m, the angle of the plane as a = 60°, the length of the plane as d = 0.30 m, the height of the table as H₂ = 1.0 m, the
initial speed of the box at the top of the plane as v₁ = 2.0m/s, and the height from part (b) as H3 = 0.90m. Use the floor as the level of zero gravitational potential energy.
Express your answer in terms of some or all of the variables m, a, d, μk, H2, v1, and the acceleration due to gravity g.
View Available Hint(s)
Hint 1. Potential and kinetic energy
The only conservative forces acting on the box in this problem are the normal force and weight. Though the normal force is indeed conservative, the work done by the
normal force is always zero, so we do not need to include any potential energy for this force, assuming that this energy is always equal to zero. Potential energy of the
gravitational force on the surface of Earth equals mgy, where y is the height of an object above the level of zero gravitational potential energy. Kinetic energy, by contrast,
does not directly depend on the position of the object and depends only on the mass and speed of the object.
Figure
1.0 m
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0.30 m
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Transcribed Image Text:Review | Constants A 60° inclined plane of length 0.30 m is positioned at the edge of a table that is 1.0 m high, as shown in (Figure 1). A box is placed at the top of the plane and given a shove so that it has an initial velocity of 2.0 m/s down the plane. The coefficient of kinetic friction between the block and the plane is μk = 0.80. (a) Calculate the speed of the block when it reaches the bottom of the plane. (b) Find the speed of the block when it is 0.90 m above the floor. (c) Is the total mechanical energy of the block conserved as it moves from the top of the plane to the floor? Write an expression for the sum of kinetic and potential energies of the box at the initial moment. Throughout the problem, we denote the mass of the box as m, the angle of the plane as a = 60°, the length of the plane as d = 0.30 m, the height of the table as H₂ = 1.0 m, the initial speed of the box at the top of the plane as v₁ = 2.0m/s, and the height from part (b) as H3 = 0.90m. Use the floor as the level of zero gravitational potential energy. Express your answer in terms of some or all of the variables m, a, d, μk, H2, v1, and the acceleration due to gravity g. View Available Hint(s) Hint 1. Potential and kinetic energy The only conservative forces acting on the box in this problem are the normal force and weight. Though the normal force is indeed conservative, the work done by the normal force is always zero, so we do not need to include any potential energy for this force, assuming that this energy is always equal to zero. Potential energy of the gravitational force on the surface of Earth equals mgy, where y is the height of an object above the level of zero gravitational potential energy. Kinetic energy, by contrast, does not directly depend on the position of the object and depends only on the mass and speed of the object. Figure 1.0 m 60% < 1 of 1 > 0.30 m K₁+U₁ = Submit ΜΕ ΑΣΦ ? α β δ € η 0 Κ λ μ ν Ρ σ τ Φ χ @ ☑ A Σ Φ ΨΩ ħ E Previous Answers Request Answer
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