Question

A. 100 kg one-man bobsled starts from rest 50 m from the end of an icy. Part A 15

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slope. A giant 20-m-lang spring is placed against a barricade at the bottom of the slope. (Figure.1) shows a coordinate system with the origin at the base of the spring. The bobsled brake falls to work, and the sled Which energies change as the bobsled moves down the slope and hits the spring? crashes into the spring. The spring comprossos 75 cm before expanding and shooting the bobsled back up the slope. What is the speing constant of the spring? Figure * Incorrect; Try Again; One attempt remaining Pecall the potential energy of a spring. Part B Complete previous part(s) Part C Complete previous part(s) Part D Complete previous part(s) Part E Complete provious part(s) Part F. Complete previous part(s)

Answer 1

As the bobsled moves down the slope and hits the spring, the potential energy and kinetic energy of the bobsled change. To find the spring constant, we can use the conservation of mechanical energy and rearrange the formula for the spring constant to solve for it. The spring constant can be calculated using the formula k = (mg(h - x))/x, where m is the mass of the bobsled, g is the acceleration due to gravity, h is the height above the ground, and x is the displacement of the spring from its equilibrium position.

Step-by-step explanation:

As the bobsled moves down the slope and hits the spring, the potential energy and kinetic energy of the bobsled change.

Initially, when the bobsled is at rest at the starting point, it has no kinetic energy but it has gravitational potential energy due to its elevation above the ground. As the bobsled moves down the slope, its potential energy decreases while its kinetic energy increases. When the bobsled reaches the spring and compresses it, some of its kinetic energy is converted into potential energy of the compressed spring. This potential energy is stored in the spring.

To calculate the spring constant, we can use the formula F = kx, where F is the force applied by the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position. In this case, the spring compresses by 75 cm, which is 0.75 m, so we can use this information to solve for the spring constant.

To find the spring constant, we can rearrange the formula to k = F/x. However, we need to determine the force applied by the spring. To do this, we can use the conservation of mechanical energy. The potential energy of the bobsled at the top of the slope is equal to the potential energy stored in the compressed spring. The potential energy can be calculated using the formula PE = mgh, where m is the mass of the bobsled, g is the acceleration due to gravity, and h is the height above the ground. We can rearrange this formula to solve for the force applied by the spring: F = mg(h - x). Substituting the given values, we can solve for the spring constant:

k = F/x = (mg(h - x))/x

Answer 2

1. The vertical height
`$h$` of the slope is approximately 12.94 meters. Using the conservation of energy principle, the spring constant
`$k$` of the spring is calculated to be approximately
`$45092 \mathrm{~N} / \mathrm{m}$`.

2. The correct option is c. Thermal energy.

The scenario described involves a physics problem where we need to find the spring constant of a spring that compresses a certain distance when impacted by a bobsled. The problem is a classic example of the conservation of mechanical energy, assuming no energy is lost due to non-conservative forces like friction or air resistance.

1. Here are the steps to solve the problem:

1. Identify the Initial and Final States: The initial state is the bobsled at rest at the top of the slope, and the final state is the bobsled compressed against the spring.

2. Calculate the Potential Energy at the Start: The gravitational potential energy at the start
`$\left(U_g\right)$` can be calculated using the formula
`$U_g=m g h$`, where
`$m$` is the mass of the bobsled,
`$g$` is the acceleration due to gravity, and
`$h$` is the vertical height of the slope which can be found from the length of the slope
`$(L)$` and the angle
`$(\theta)$`.

3. Calculate the Kinetic Energy Just Before Impact: As the bobsled slides down the slope, it converts potential energy into kinetic energy. Just before impact, all the potential energy will have been converted to kinetic energy
`$(K)$`, which is given by
`$K=(1)/(2) m v^2$`.

4. Apply the Conservation of Energy Principle: At the point of maximum compression, all the kinetic energy will have been converted into elastic potential energy stored in the spring
`$\left(U_s\right)$`, which is given by
`$U_s=(1)/(2) k x^2$`, where
`$k$` is the spring constant, and
`$x$` is the compression of the spring.

5. Set up the Equation and Solve for
`$k$` : Since energy is conserved,
`$U_g$` at the start will be equal to
`$U_s$` at the point of maximum compression. We can set up the equation
`$m g h=(1)/(2) k x^2$` and solve for
`$k$`.

Calculations based on the given information:

• Mass of the bobsled,
  `$m=100 \mathrm{~kg}$`
• Length of the slope,
  `$L=50 \mathrm{~m}$`
• Angle of the slope,
  `$\theta=15^(\circ)$`
• Compression of the spring,
  `$x=75 \mathrm{~cm}=0.75 \mathrm{~m}$`
• Acceleration due to gravity,
  `$g=9.8 \mathrm{~m} / \mathrm{s}^2$`

Let's find the height
`$h$` using the angle
`$\theta$` and the length
`$L$`, and then calculate the spring constant
`$k$`.

1. The height $h$ from which the bobsled starts sliding is calculated using the sine component of the angle, which gives us
`$h=50 * \sin \left(15^(\circ)\right) \approx 12.94$` meters.

2. Using the potential energy formula
`$U_g=m g h$`, we find the total potential energy at the top of the slope.

3. Knowing that this potential energy converts into elastic potential energy at maximum compression, we set the gravitational potential energy equal to the spring's elastic potential energy,
`$(1)/(2) k x^2$`.

4. Solving for
`$k$` gives us the spring constant, which is approximately
`$45092 \mathrm{~N} / \mathrm{m}$`.

So, the spring constant of the spring is around
`$45092 \mathrm{~N} / \mathrm{m}$`.

2. As the bobsled moves down the slope and hits the spring, the following types of energy change:

1. Gravitational Potential Energy: This decreases as the bobsled moves down the slope because the height with respect to the ground is decreasing.

2. Kinetic Energy: This increases as the bobsled moves down the slope because it is accelerating due to gravity and converting potential energy into kinetic energy.

3. Elastic Potential Energy: This increases only when the bobsled contacts and compresses the spring. Before contact with the spring, there is no elastic potential energy involved.

4. Thermal Energy: Although not explicitly stated in the problem, in a real-world scenario, thermal energy would increase due to friction between the bobsled and the slope, as well as within the spring as it compresses and then decompresses.

In a theoretical, ideal scenario where non-conservative forces like friction are ignored (which is often the case in physics problems unless otherwise stated), the only energies considered to change would be gravitational potential energy, kinetic energy, and elastic potential energy. However, if we consider a realistic scenario, then thermal energy would also increase due to frictional forces.

The complete question is here: