A 0.097 kg cup falls from the kitchen shelf and shatters on the ceramic tile floor. Assume that the maximum kinetic energy obtained by the cup is 2.6 J and that air resistance is negligible. Calculate the cup's maximum speed
Why did the cup fall from the kitchen shelf? Maybe it just couldn't handle the pressure of holding all those cups and plates on top of it. Poor cup, it just couldn't cup with the responsibility. But don't worry, I've got your back. Let's calculate the cup's maximum speed!
To find the maximum speed (v) of the cup, we can use the formula for kinetic energy:
KE = (1/2)mv^2
Where:
KE = kinetic energy
m = mass of the cup
v = speed of the cup
Given that the maximum kinetic energy obtained by the cup is 2.6 J and the mass of the cup is 0.097 kg, we can rearrange the equation to solve for v:
2.6 J = (1/2)(0.097 kg)(v^2)
Now, let's do some math! Don't worry, I'll keep it simple, like a cup of tea.
v^2 = (2.6 J) / (0.097 kg)(1/2)
v^2 = 53.608
v ≈ √53.608
v ≈ 7.325 m/s
So, the cup's maximum speed is approximately 7.325 meters per second. That's quite a speedy cup! Just remember, it's always good to keep your cups on steady ground or they might find themselves in a shattered situation again. Stay safe!
To calculate the cup's maximum speed, we can use the formula for kinetic energy:
KE = (1/2) * m * v^2
Where:
KE is the kinetic energy (2.6 J),
m is the mass of the cup (0.097 kg),
and v is the velocity (maximum speed) of the cup.
Rearranging the equation, we can solve for v:
v^2 = (2 * KE) / m
Plugging in the given values, we get:
v^2 = (2 * 2.6 J) / 0.097 kg
v^2 = 53.6 J/kg
Taking the square root, we find:
v ≈ √(53.6 J/kg)
Therefore, the cup's maximum speed is approximately 7.32 m/s.
To calculate the cup's maximum speed, we can use the formula for kinetic energy.
The formula for kinetic energy is given by:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass of the object, and v is the velocity (speed) of the object.
In this case, we are given the mass of the cup (m = 0.097 kg) and the maximum kinetic energy (KE = 2.6 J).
Rearranging the formula, we get:
v^2 = (2 * KE) / m
Substituting the given values into the formula, we have:
v^2 = (2 * 2.6 J) / 0.097 kg
Simplifying further, we have:
v^2 = 53.61
To find the maximum speed (v), we take the square root of both sides:
v = √(53.61)
Calculating this, we find:
v ≈ 7.33 m/s
Therefore, the cup's maximum speed when it falls from the kitchen shelf and shatters on the ceramic tile floor is approximately 7.33 m/s.
(1/2)*M(Vmax)^2 = 2.6 joules
Solve for Vmax, in m/s
Ek= 1/2mV^
2.6J= 1/2(0.097)v^
2(2.6)/0.097= v^
53.7=V^
V=7.3m/s