A 10-kg mass is projected straight up with a speed of 20.0 meter/second.
1. Find the initial kinetic energy of the mass
2. To what height does the mass rise?
1. KE = 0.5m*V^2 = 5*20^2 = 2000 Joules
2. V^2 = Vo^2 + 2g*h =
h = (V^2-Vo^2)/2g
h = (0-20^20/-19.6 = 20.4 m.
Correction: h = (0-20^2)/-19.6 = 20.4 m.
To solve both of these questions, we can use the principles of energy conservation, specifically the conservation of mechanical energy.
1. Find the initial kinetic energy of the mass:
The initial kinetic energy of an object can be calculated using the formula:
Kinetic Energy = 0.5 * mass * velocity^2
Here the mass is 10 kg and the velocity is 20.0 m/s. Plugging these values into the formula:
Kinetic Energy = 0.5 * 10 kg * (20.0 m/s)^2
= 0.5 * 10 kg * 400 m^2/s^2
= 2000 J (joules)
So, the initial kinetic energy of the mass is 2000 joules.
2. To what height does the mass rise:
To find the height to which the mass rises, we can use the conservation of mechanical energy. When the mass is at its highest point, it has no kinetic energy since its velocity is zero. Therefore, all of its initial kinetic energy is converted into potential energy.
The potential energy of an object at a certain height can be calculated using the formula:
Potential Energy = mass * acceleration due to gravity * height
Here the mass is 10 kg, and the acceleration due to gravity on Earth is approximately 9.8 m/s^2. Let's assume that the height is h. So, the potential energy at the highest point is:
Potential Energy = 10 kg * 9.8 m/s^2 * h
Since the initial kinetic energy is equal to the potential energy at the highest point, we can equate the two values:
2000 J = 10 kg * 9.8 m/s^2 * h
Simplifying the equation:
2000 J = 98 kg m^2/s^2 * h
Dividing both sides of the equation by 98 kg m^2/s^2:
h = 2000 J / (98 kg m^2/s^2)
≈ 20.41 m
So, the mass rises to a height of approximately 20.41 meters.