Question

how fast, in meters per second, is object a moving at the end of the ramp if it's mass is 115 g, it's radius 17 cm, and the height of the beginning of the ramp is 14 cm?

Answer 1

Object A is moving at approximately
`\(0.59 \ m/s\)` at the end of the ramp.

Step-by-step explanation:

The final velocity of object A at the end of the ramp can be determined using the principles of energy conservation. Initially, the potential energy
`(\(PE\))` is given by the equation
`\(PE = mgh\), where \(m\)` is the mass,
`\(g\)` is the acceleration due to gravity, and
`\(h\)` is the height. The potential energy is then converted into kinetic energy
`(\(KE\))` at the bottom of the ramp, where
`\(KE = (1)/(2)mv^2\), with \(v\)` being the final velocity.

First, we calculate the potential energy at the beginning of the ramp:

`\[PE = mgh = (0.115 \ kg)(9.8 \ m/s^2)(0.14 \ m) = 0.16078 \ J.\]`

Next, we equate the potential energy to the kinetic energy at the bottom of the ramp:

`\[0.16078 \ J = (1)/(2)(0.115 \ kg)v^2.\]`

Solving for
`\(v\),` we find:

`\[v = \sqrt{(2(0.16078 \ J))/(0.115 \ kg)} \approx 0.588 \ m/s.\]`

Therefore, object A is moving at approximately
`\(0.59 \ m/s\)` at the end of the ramp.

In summary, by applying the principles of energy conservation, we determined the final velocity of object A by equating potential energy to kinetic energy. The mass, gravity, and height of the ramp were considered in the calculations to find the velocity of the object.

Answer 2

To calculate the speed of object A at the end of the ramp, we can use the principle of conservation of energy. The potential energy at the beginning of the ramp is equal to the sum of the kinetic energy and potential energy at the end of the ramp. Plugging in the given values, we find that object A is moving at approximately 1.949 m/s at the end of the ramp.

Step-by-step explanation:

To calculate the speed of object A at the end of the ramp, we can use the principle of conservation of energy. The potential energy at the beginning of the ramp is equal to the sum of the kinetic energy and potential energy at the end of the ramp.

First, let's convert the mass of object A to kilograms by dividing it by 1000: 115 g = 0.115 kg.

The potential energy at the beginning of the ramp is given by: mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the ramp. Plugging in the values, we get: (0.115 kg)(9.8 m/s²)(0.14 m) = 0.15994 J.

The potential energy at the end of the ramp is given by: mgh, where h is the vertical distance between the beginning and end of the ramp. Plugging in the values, we get: (0.115 kg)(9.8 m/s²)(0.14 m + 0.17 m) = 0.2189 J.

The kinetic energy at the end of the ramp is given by: (1/2)mv^2, where m is the mass and v is the velocity. Plugging in the values, we get: (1/2)(0.115 kg)v² = 0.2189 J.

Simplifying the equation, we find: v² = (0.2189 J) / (1/2)(0.115 kg) = 3.797 m²/s².

Taking the square root of both sides, we get: v ≈ 1.949 m/s.