When a 1.50 kg block is 3.96 m above the base of the hill, the mass has a speed of 1.71 m/s. When the block reaches a point 0.750 m above the base of the hill, what is its kinetic energy?

Searches related to A block is sliding down a frictionless hill. When the 1.50 kg block is 3.96 m above the base of the hill, the mass has a speed of 1.71 m/s. Determine the kinetic energy of the block when it is at a height of 0.750 m above the base of the hill.

To find the kinetic energy of the block at a certain height, we need to understand the relationship between kinetic energy and gravitational potential energy.

The kinetic energy (KE) of an object is given by the equation:

KE = (1/2) * m * v^2

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

At any given height above the base of the hill, the total mechanical energy (which is the sum of kinetic energy and gravitational potential energy) remains constant. In other words:

KE + PE = constant

Where PE is the potential energy, given by the equation:

PE = m * g * h

Where g is the acceleration due to gravity (9.8 m/s^2) and h is the height above the base of the hill.

Now let's calculate the kinetic energy of the block when it reaches a point 0.750 m above the base of the hill.

Given:
Mass of the block, m = 1.50 kg
Height above the base of the hill, h = 0.750 m
Velocity, v = 1.71 m/s

First, let's calculate the kinetic energy at the initial height (3.96 m above the base of the hill). We'll use the equation KE = (1/2) * m * v^2.

KE_initial = (1/2) * 1.50 kg * (1.71 m/s)^2

KE_initial = 2.5 J (Joules)

Now, using the conservation of energy principle, we can find the potential energy at the initial height:

PE_initial = KE_initial - KE_final

Where KE_final is the kinetic energy at the final height (0.750 m above the base of the hill) that we want to calculate.

PE_initial = m * g * h_initial - KE_final
PE_initial = 1.50 kg * 9.8 m/s^2 * 3.96 m - KE_final

Now, let's rearrange the equation to find KE_final:

KE_final = 1.50 kg * 9.8 m/s^2 * 3.96 m - PE_initial

Substituting the given values:

KE_final = 1.50 kg * 9.8 m/s^2 * 0.750 m - 2.5 J

Calculating:

KE_final = 11.03 J (Joules)

Therefore, the kinetic energy of the block when it reaches a point 0.750 m above the base of the hill is 11.03 Joules.

KE gain= gpe loss

ke gain =m*g*(3.96-.750)