Consider a system of a cliff diver and the earth. The gravitational potential energy of the system decreases by 21,000 J as the diver drops to the water from a height of 32.0 m. Determine her weight in newtons.
To determine the weight of the diver in newtons, we need to use the equation for gravitational potential energy:
Gravitational potential energy = mgh,
where m is the mass of the diver, g is the acceleration due to gravity, and h is the height of the cliff.
Given that the gravitational potential energy decreases by 21,000 J and the height of the cliff is 32.0 m, we can write the equation as:
21,000 J = mgh.
To find the weight of the diver, we need to convert the gravitational potential energy into weight. The formula relating gravitational potential energy to weight is:
Weight = m × g,
where g is the acceleration due to gravity. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Substituting the values into the equation, we can solve for the weight:
21,000 J = m × 9.8 m/s^2 × 32.0 m.
Dividing both sides of the equation by (9.8 × 32.0), we get:
m = 21,000 J / (9.8 m/s^2 × 32.0 m).
Calculating the right side of the equation:
m = 68.45 kg.
Finally, substituting the mass into the equation for weight:
Weight = m × g = 68.45 kg × 9.8 m/s^2.
Calculating the weight:
Weight = 670.81 N.
Hence, the weight of the diver is approximately 670.81 Newtons.
To determine the weight of the cliff diver in newtons, we need to use the relation between gravitational potential energy (PE), weight (W), and height (h) given by the formula:
PE = mgh
Where:
PE is the gravitational potential energy measured in joules (J),
m is the mass of the object in kg,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
and h is the height in meters.
In this case, we are given that the gravitational potential energy decreases by 21,000 J, and the height is 32.0 m. So we can set up the equation as follows:
PE = 21,000 J
h = 32.0 m
g = 9.8 m/s^2
Solving the formula for weight:
PE = mgh
21,000 J = mg(32.0 m)
21,000 J = 9.8 m/s^2 * m * 32.0 m
Now we can solve for the weight (W) in newtons:
21,000 J = 313.6 m^2
Divide both sides of the equation by 313.6:
(21,000 J) / (313.6 m^2) = m
Using a calculator, we find:
m ≈ 66.925 kg
Finally, we can calculate the weight (W) using the formula:
W = mg
W = (66.925 kg) * (9.8 m/s^2)
Using a calculator, we find:
W ≈ 656.745 N
Therefore, the cliff diver's weight is approximately 656.745 newtons.