Question

A 2 kg ball is at the top of a ramp that is 5 m tall. How fast will that ball be going when it is halfway down the ramp?

Answer 1

when the ball is halfway down the ramp, it will be going at a speed of 7 m/s.

Step-by-step explanation:

To determine the speed of a 2 kg ball when it is halfway down a 5 m tall ramp, we can use the principles of conservation of energy and kinematics.

At the top of the ramp, the ball has gravitational potential energy given by:

PE = mgh

where m is the mass of the ball (2 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the ramp (5 m). Plugging in these values, we get:

PE = (2 kg)(9.8 m/s^2)(5 m) = 98 J

As the ball rolls down the ramp, some of this potential energy is converted into kinetic energy, which is given by:

KE = (1/2)mv^2

where v is the velocity of the ball. At any point along the ramp, the total energy (potential plus kinetic) of the ball remains constant. Therefore, we can set the initial potential energy equal to the sum of kinetic and potential energies at any point along the ramp.

When the ball is halfway down the ramp, it has descended a height of 2.5 m. Its potential energy at this point is:

PE = (2 kg)(9.8 m/s^2)(2.5 m) = 49 J

Therefore, its kinetic energy at this point must also be 49 J. Plugging this into our equation for kinetic energy, we get:

49 J = (1/2)(2 kg)v^2

Solving for v, we get:

v = sqrt(98/2) = sqrt(49) = 7 m/s

Answer 2

The ball will be going approximately 9.90 m/s when it is halfway down the ramp.

The speed of the ball when it is halfway down the ramp can be determined using the principle of conservation of energy. As the ball moves down the ramp, its potential energy is converted into kinetic energy.

First, calculate the potential energy of the ball at the top of the ramp using the formula PE = mgh, where m is the mass of the ball (2 kg), g is the acceleration due to gravity (
`9.8 m/s^2`), and h is the height of the ramp (5 m).

`PE = (2 kg)(9.8 m/s^2)(5 m) = 98 J`

Next, determine the kinetic energy of the ball when it is halfway down the ramp. At this point, all of the ball's potential energy is converted into kinetic energy. Therefore, KE = PE.

KE = 98 J

The kinetic energy of an object can be calculated using the formula
`KE = ((1)/(2))mv^2`,

where m is the mass of the object and v is its velocity.

`((1)/(2))mv^2 = 98 J`

Solve for v:

`v^2 = ((2 * 98 J))/(2 kg) = (98 m^2)/(s^2)`

`v = \sqrt(98 m^2)/(s^2) \approx 9.90 m/s`

Therefore, the ball will be going approximately 9.90 m/s when it is halfway down the ramp.