A 2.48-kg rock is released from rest at a height of 28.1 m. Ignore air resistance and determine (a) the kinetic energy at 28.1 m, (b) the gravitational potential energy at 28.1 m, (c) the total mechanical energy at 28.1 m, (d) the kinetic energy at 0 m, (e) the gravitational potential energy at 0 m, and (f) the total mechanical energy at 0 m.
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To find the answers to these questions, we need to use certain formulas related to kinetic energy and gravitational potential energy.
(a) The formula for kinetic energy is given by K.E. = (1/2) * m * v^2, where m is the mass of the object and v is its velocity.
To find the kinetic energy at 28.1 m, we need to first find the velocity of the rock when it reaches that height. We can use the conservation of energy principle, which states that the total mechanical energy (potential energy + kinetic energy) of a system remains constant if no external forces are acting on it.
(c) The total mechanical energy at 28.1 m can be calculated using the formula E = K.E. + G.P.E., where E represents the total mechanical energy, K.E. is the kinetic energy, and G.P.E. is the gravitational potential energy.
To find the gravitational potential energy at 28.1 m, we can use the formula G.P.E. = m * g * h, where g is the acceleration due to gravity (9.8 m/s^2) and h is the height.
Now, let's calculate each of the required values:
(a) Kinetic energy at 28.1 m:
To find the velocity at that height, we can use the equation for potential energy:
G.P.E. = m * g * h
28.1 m * (9.8 m/s^2) = 2.48 kg * g * h
h = (28.1 m * 9.8 m/s^2) / (2.48 kg * 9.8 m/s^2)
h = 11.2903 m
Now, we can use the conservation of energy principle to calculate the kinetic energy at 28.1 m:
K.E. = E - G.P.E.
K.E. = E - m * g * h
K.E. = E - (2.48 kg * 9.8 m/s^2 * 11.2903 m)
(b) Gravitational potential energy at 28.1 m:
G.P.E. = m * g * h
G.P.E. = 2.48 kg * 9.8 m/s^2 * 28.1 m
(c) Total mechanical energy at 28.1 m:
E = K.E. + G.P.E.
E = K.E. + m * g * h
To find the values at 0 m (the starting position), we can simply substitute h = 0 into the formulas from above:
(d) Kinetic energy at 0 m:
Since the object is released from rest (meaning it has no initial velocity), the kinetic energy at 0 m is zero.
(e) Gravitational potential energy at 0 m:
G.P.E. = m * g * h
G.P.E. = 2.48 kg * 9.8 m/s^2 * 0 m
(f) Total mechanical energy at 0 m:
E = K.E. + G.P.E.
E = 0 + m * g * h
By plugging in the values and performing the calculations, you can find the numerical answers for each part of the question.