when a ball is dropped throuh a height, its potential energy changes. Suppose all this energy gets converted into internal energyof the ball once it has stopped bouncing and the specfic heat of the vall is 0.850 j/g-k(no heat loss to the environment). Calculate the height from wich the ball must be dropped to increase its temp. by 1.00 degree c?
b) At what velocity must a 20.0g object be moving to posssess a kinetic energy of 1.00 J?
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To calculate the height from which the ball must be dropped to increase its temperature by 1.00 degree Celsius, we need to consider the energy conversions involved.
First, let's calculate the amount of heat energy required to increase the temperature of the ball. We can use the specific heat formula:
Q = m * c * ΔT
where Q is the heat energy, m is the mass of the ball, c is the specific heat, and ΔT is the change in temperature.
In this case, the mass of the ball is not given, but we can assume it to be 1 gram for simplicity:
Q = 1g * 0.850 J/g-K * 1.00 °C = 0.850 J
Next, we need to find the gravitational potential energy (PE) of the ball when it is dropped from a certain height. The formula for potential energy is:
PE = m * g * h
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s²), and h is the height.
Now, we need to equate the heat energy (Q) to the potential energy (PE) when the ball comes to rest on the ground:
Q = PE
0.850 J = m * g * h
Since we assumed the mass of the ball to be 1 gram:
0.850 J = (1g) * (9.8 m/s²) * h
Simplifying, we get:
h = 0.850 J / (1g * 9.8 m/s²) = 0.0867 meters
Therefore, the ball must be dropped from a height of approximately 0.087 meters to increase its temperature by 1.00 degree Celsius.
b) To calculate the velocity at which a 20.0g object must be moving to possess a kinetic energy of 1.00 J, we can use the formula for kinetic energy:
KE = 1/2 * m * v²
where KE is the kinetic energy, m is the mass of the object, and v is the velocity.
Rearranging the formula:
v² = (2 * KE) / m
v = sqrt((2 * KE) / m)
Plugging in the values:
v = sqrt((2 * 1.00 J) / 20.0g)
v = sqrt(0.1 J/g)
v = 0.316 m/s
Therefore, the object must be moving at a velocity of approximately 0.316 m/s to possess a kinetic energy of 1.00 J.