Physics energy questions

Question

1.What is the potential energy of a 300 kg boulder that sits on the edge of a 25 m tall cliff?

2.A person eats an 199,000 J snack before working out. If the person uses all of their eaten energy to lift a 14 kg weight. How high can they lift the weight?

3.A spring has 2,208 J of energy stored in it. It launches a block 15.7 m into the air (straight up). How much mass must the block have?

*answer and explanation please*

Answer 1

1). Gravitational potential energy is stored energy that has the "potential" for movement when it is at rest a certain height about the earth. The formula is:

P.E. = U = m*g*h

where m is the mass of the object, h is the height about the earth, and g is the acceleration due to gravity of g=9.8 m/s^2.

Thus PE=(300 kg)*(9.8 m/s^2)*(25 m)= 73500 kg*m^2/s^2 = 73500 J

2). The energy from the snack can be though of as potential energy of the body to lift the weight. All the snack energy is converted to potential energy to lift the weight, so

PE of snack = mass weight*g*height of the weight (aka, PE=mgh)

Solving for height of the weight:

height of weight = PEsnack/(mass weight *g) = (199,000 kg*m^2/s^2)/(14 kg * 9.8 m/s^2) = 1450 m

3). The stored energy of a spring is PEspring=1/2kx^2 where k is the spring constant x is the distance the spring is compressed. However, we do not know the amount the spring is compressed or the constant k, but rather we know the amount of energy the spring is storing already as 2,208 J = 1/2 kx^2

The important part of this question is that the spring energy is converted into kinetic energy of motion and potential energy of a height above the earth (i.e., straight up into the air). From kinematics, we know that the block will move with a velocity up into the air and reach a height 15.7 m, at which point its velocity is 0 m/s. Thus, the block now has gravitational potential energy PE=mgh at that point.

This is a conservation of energy problem between the PE of the spring and the gravitational PE.

Einitial=Efinal

PEspring=PEgrav

PEspring=mgh

But we are looking for the mass of the block. Solving algebraically, we get:

m=PEspring/(g*h)=(2208 J) / (9.8 m/s^2 * 15.7 m) = 14.4 kg

Answer 2

Mechanical energy falls into 2 basic categories: Potential, and Kinetic.

Potential Energy exists in any situation where there is a force that can act through a distance. The most common example is an object held at some height above a reference plane. The force is the gravitational pull on the object and the distance is the height.

The other common example is the compression of a spring.

The MKS unit of energy is the Joule, which is 1 Newton-meter. We can relate to this by recognizing that a common example of work is pushing or lifting and object some distance.

The questions:

1. First, find the gravitational force on the mass. F = ma, where a is the acceleration of gravity. Then multiply by the distance (in this case, the height above the ground.
2. First find the force of gravity on the weight. Divide that into the given number of Joules to the get the distance
3. The energy stored in the spring is initially converted to kinetic energy. When the block reaches its maximum height, the kinetic energy has all been converted to potential energy, which is the product of the height, and the force of gravity.

In all cases, pay attention to the units. For example, 1 Newton is 9.8 times the mass in kilograms.