A 0.4-kg ball has a velocity of 20 m/s.
a. What is the kinetic energy of the ball?
b. How much work was required to lift the box to this position?
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a) Kinetic Energy = (1/2) M V^2
Have you never seen that formula before?
Well, now you have.
b) How far (vertically) was it lifted? Compute the potential energy dfference.
That will be the answer.
How did the ball turn into a box?
To answer the questions, we will need to use the formulas for kinetic energy and work.
a. The kinetic energy (KE) of an object can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Let's plug in the given values:
mass = 0.4 kg
velocity = 20 m/s
KE = (1/2) * 0.4 kg * (20 m/s)^2
KE = 0.5 * 0.4 kg * 400 m^2/s^2
KE = 80 J
Therefore, the kinetic energy of the ball is 80 Joules (J).
b. The work (W) done to lift the box is equal to the change in potential energy. The formula to calculate work is:
W = m * g * h
Where:
m = mass (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height or vertical displacement (in meters)
Since the question does not mention any height or vertical displacement, we cannot calculate the work required to lift the box to a particular position.
To find the answer to these questions, you need to apply the formulas for kinetic energy and work.
a. The formula for kinetic energy (KE) is:
KE = 0.5 * mass * velocity^2
In this case, the given values are:
mass = 0.4 kg
velocity = 20 m/s
Plugging these values into the formula, we have:
KE = 0.5 * 0.4 kg * (20 m/s)^2
Simplifying this equation, we get:
KE = 0.5 * 0.4 kg * 400 m^2/s^2
KE = 80 J (joules)
Therefore, the kinetic energy of the ball is 80 joules.
b. The formula for work (W) is:
W = force * distance * cos(theta)
In this case, the force required to lift the box is equal to the weight of the box, which is given by:
Force = mass * gravity
The given values are:
mass = 0.4 kg
gravity = 9.8 m/s^2 (approximate value for acceleration due to gravity on Earth)
Plugging these values into the formula, we have:
Force = 0.4 kg * 9.8 m/s^2
Force = 3.92 N (newtons)
Now, we need to find the distance and the angle (theta). The given question does not provide these values, so you need to consult the problem statement or any additional information to determine them.
Once you have the values, you can plug them into the work formula to find the answer.
But since the necessary information is missing, we cannot determine the work required to lift the box to this position.
In summary:
a. The kinetic energy of the ball is 80 joules.
b. The work required to lift the box to this position cannot be determined without the distance and angle information.