1. A body was dropped from a building 10-m high. Its kinetic energy before reaching the ground is 980 J. What is the mass of the body?
2. A 1.0-kg block slides down a rough inclined plane whose height is 1.0 m. At the bottom the block has a speed of 4.0 m/s. Is mechanical energy conserved? Explain your answer and justify.
1. V^2 = Vo^2 + 2g*h = 0 + 19.6*10 = 196
V = 14 m/s.
KE = 0.5m*V^2 = 980 J.
0.5M*196 = 980
M = 980/(0.5*196) = 10 kg.
2. PE = mg*h = 9.8*1 = 9.8 J. At top of
inclined plane.
KE = 0.5m*V^2 = 0.5 * 1 * 4^2 = 8.0 J. At bottom of inclined plane.
9.8 - 8.0 = 1.8 J. Lost to heat caused by friction.
1. KE = PE = M*9.8*10 = 980.
KE = 10 kg.
1. To find the mass of the body, we can use the equation for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
The given kinetic energy is 980 J, so we have:
980 J = (1/2) * mass * velocity^2
Since the body was dropped, the initial velocity is 0. However, we know that the final velocity is related to the height of the building via the equation:
Final Velocity = sqrt(2 * acceleration * height)
Since the body is dropped, the acceleration is due to gravity which is approximately 9.8 m/s^2. Plugging in the given height of 10 m, we have:
Final Velocity = sqrt(2 * 9.8 m/s^2 * 10 m) = sqrt(196 m^2/s^2) = 14 m/s
Substituting this into the equation for kinetic energy, we have:
980 J = (1/2) * mass * (14 m/s)^2
Simplifying this equation gives us:
980 J = 98 * mass
Now we can solve for the mass:
mass = 980 J / 98 = 10 kg
Therefore, the mass of the body is 10 kg.
2. To determine whether mechanical energy is conserved, we need to consider the work done by non-conservative forces such as friction.
First, we define mechanical energy as the sum of potential energy and kinetic energy:
Mechanical Energy = Potential Energy + Kinetic Energy
At the bottom of the incline, the block has 4.0 m/s of kinetic energy. The potential energy at the top of the ramp is given by:
Potential Energy = mass * gravity * height
Substituting the given mass (1.0 kg), gravity (9.8 m/s^2), and height (1.0 m) into the equation gives us:
Potential Energy = 1.0 kg * 9.8 m/s^2 * 1.0 m = 9.8 J
The total mechanical energy at the bottom of the ramp is therefore:
Mechanical Energy = 9.8 J (Potential Energy) + 4.0 J (Kinetic Energy) = 13.8 J
Now, we need to consider the work done by non-conservative forces. If the inclined plane is rough, there might be friction present, which would do work on the block. If friction does work, it will decrease the mechanical energy of the block. In this case, mechanical energy is not conserved.
To determine if friction is present and doing work, additional information is required, such as the coefficient of friction or the work done by friction. Without that information, we cannot definitively say if mechanical energy is conserved or not.