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Math  /  Algebra

Question1. (I) By how much does the gravitational potential energy of a 58−kg58-\mathrm{kg} pole vaulter change if her center of mass rises 4.0 m during the jump?

Studdy Solution

STEP 1

1. The mass of the pole vaulter is 58 kg 58 \, \text{kg} .
2. The center of mass of the pole vaulter rises by 4.0 m 4.0 \, \text{m} .
3. The acceleration due to gravity is 9.8 m/s2 9.8 \, \text{m/s}^2 .
4. We are calculating the change in gravitational potential energy.

STEP 2

1. Identify the formula for gravitational potential energy.
2. Substitute the known values into the formula.
3. Calculate the change in gravitational potential energy.

STEP 3

Identify the formula for gravitational potential energy.
The gravitational potential energy U U is given by the formula: U=mgh U = mgh
where m m is the mass, g g is the acceleration due to gravity, and h h is the height.

STEP 4

Substitute the known values into the formula.
Given: - m=58 kg m = 58 \, \text{kg} - g=9.8 m/s2 g = 9.8 \, \text{m/s}^2 - h=4.0 m h = 4.0 \, \text{m}
Substitute these values into the formula: U=58×9.8×4.0 U = 58 \times 9.8 \times 4.0

STEP 5

Calculate the change in gravitational potential energy.
U=58×9.8×4.0=2273.6 J U = 58 \times 9.8 \times 4.0 = 2273.6 \, \text{J}
The change in gravitational potential energy is:
2273.6 J \boxed{2273.6 \, \text{J}}

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