To solve this problem, we can use the principle of conservation of energy. The box starts with potential energy and ends with kinetic energy, since there is no friction to convert some of the energy into heat.

Step 1: Calculate the initial potential energy (PE) of the box at the top of the ramp. The formula for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

The height can be calculated using the sine of the angle of the ramp (sin(10°) = h/6.0m). So, h = 6.0m * sin(10°) = 1.04m.

So, PE = 10.0kg * 9.8m/s² * 1.04m = 102.08 Joules.

Step 2: At the bottom of the ramp, all the potential energy has been converted into kinetic energy (KE). The formula for kinetic energy is KE = 1/2 * m * v², where m is the mass and v is the velocity.

Setting the potential energy equal to the kinetic energy gives us 102.08 J = 1/2 * 10.0kg * v².

Step 3: Solve for v.

v² = 2 * 102.08 J / 10.0kg = 20.416 m²/s².

Taking the square root of both sides gives v = √20.416 m²/s² = 4.52 m/s.

So, the velocity of the crate at the bottom of the ramp is approximately 4.5 m/s. The closest answer is (a) 4.5 m/s.

Question

To solve this problem, we can use the principle of conservation of energy. The box starts with potential energy and ends with kinetic energy, since there is no friction to convert some of the energy into heat.

Step 1: Calculate the initial potential energy (PE) of the box at the top of the ramp. The formula for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

The height can be calculated using the sine of the angle of the ramp (sin(10°) = h/6.0m). So, h = 6.0m * sin(10°) = 1.04m.

So, PE = 10.0kg * 9.8m/s² * 1.04m = 102.08 Joules.

Step 2: At the bottom of the ramp, all the potential energy has been converted into kinetic energy (KE). The formula for kinetic energy is KE = 1/2 * m * v², where m is the mass and v is the velocity.

Setting the potential energy equal to the kinetic energy gives us 102.08 J = 1/2 * 10.0kg * v².

Step 3: Solve for v.

v² = 2 * 102.08 J / 10.0kg = 20.416 m²/s².

Taking the square root of both sides gives v = √20.416 m²/s² = 4.52 m/s.

So, the velocity of the crate at the bottom of the ramp is approximately 4.5 m/s. The closest answer is (a) 4.5 m/s.

Knowee AI · Accepted Answer

To solve this problem, we can use the principle of conservation of energy. The box starts with potential energy and ends with kinetic energy, since there is no friction to convert some of the energy into heat.

Step 1: Calculate the initial potential energy (PE) of the box at the top of the ramp. The formula for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

The height can be calculated using the sine of the angle of the ramp (sin(10°) = h/6.0m). So, h = 6.0m * sin(10°) = 1.04m.

So, PE = 10.0kg * 9.8m/s² * 1.04m = 102.08 Joules.

Step 2: At the bottom of the ramp, all the potential energy has been converted into kinetic energy (KE). The formula for kinetic energy is KE = 1/2 * m * v², where m is the mass and v is the velocity.

Setting the potential energy equal to the kinetic energy gives us 102.08 J = 1/2 * 10.0kg * v².

Step 3: Solve for v.

v² = 2 * 102.08 J / 10.0kg = 20.416 m²/s².

Taking the square root of both sides gives v = √20.416 m²/s² = 4.52 m/s.

So, the velocity of the crate at the bottom of the ramp is approximately 4.5 m/s. The closest answer is (a) 4.5 m/s.

A 10.0-kg box starts at rest and slides 6.0 m down a ramp inclined at an angle of 10° with the horizontal. If there is no friction between the ramp surface and crate, what is the velocity of the crate at the bottom of the ramp? (g = 9.8 m/s2)Select one:a.4.5 m/sb.10.7 m/sc.3.5 m/sd.6.1 m/s

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