A shot-putter puts a shot (weight = 71.3 N) that leaves his hand at distance of 1.62 m above the ground.
(a) Find the work done by the gravitation force when the shot has risen to a height of 2.08 m above the ground. Include the correct sign for work.
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(b) Determine the change (ÄPE = PEf - PE0) in the gravitational potential energy of the shot.
To find the work done by the gravitational force, we can use the formula:
Work = Force * Distance * cosθ
In this case, the force is the weight of the shot, which is 71.3 N. The distance is the vertical distance the shot has risen, which is 2.08 m - 1.62 m = 0.46 m. The angle between the force and the direction of motion is 0 degrees because the force is acting vertically downward and the displacement is also vertically upward. Therefore, the cosine of 0 degrees is 1.
(a) So, the work done by the gravitational force can be calculated as:
Work = 71.3 N * 0.46 m * cos(0°)
Work = 32.78 J
The correct sign for work should be negative because the gravitational force and the displacement are in opposite directions.
Therefore, the work done by the gravitational force is -32.78 J.
(b) The change in gravitational potential energy (ΔPE) of the shot can be calculated using the formula:
ΔPE = m * g * Δh
Where m is the mass of the shot, g is the acceleration due to gravity, and Δh is the change in height.
Since we know the weight of the shot, we can use the formula:
Weight = m * g
Dividing both sides by g will give us the mass (m) of the shot.
m = Weight / g
m = 71.3 N / 9.8 m/s²
m ≈ 7.28 kg
Now we can calculate the change in gravitational potential energy:
ΔPE = m * g * Δh
ΔPE = 7.28 kg * 9.8 m/s² * (2.08 m - 1.62 m)
ΔPE ≈ 28.82 J
Therefore, the change in gravitational potential energy of the shot is approximately 28.82 J.
To find the work done by the gravitational force when the shot has risen to a height of 2.08 m above the ground, we need to calculate the work done against gravity.
(a) Work done by gravity can be calculated using the formula:
Work = force × distance × cos(angle)
Since the shot is moving vertically upward, the angle between the force of gravity and the displacement is 180 degrees (opposite direction), so cos(180) = -1.
Given:
Force = 71.3 N
Distance = 2.08 m
Work = 71.3 N × 2.08 m × (-1)
Work = -148.0244 J
Therefore, the work done by the gravitational force is -148.0244 Joules.
(b) The change in gravitational potential energy (ΔPE) can be calculated using the formula:
ΔPE = m × g × Δh
Given:
Mass (m) is not provided
Acceleration due to gravity (g) = 9.8 m/s^2
Change in height (Δh) = 2.08 m - 1.62 m = 0.46 m
To find the mass (m), we need to use the formula for weight:
Weight = mass × g
Given:
Weight = 71.3 N
g = 9.8 m/s^2
71.3 N = m × 9.8 m/s^2
m = 71.3 N / 9.8 m/s^2
m = 7.28 kg
Now, we can calculate the change in potential energy:
ΔPE = 7.28 kg × 9.8 m/s^2 × 0.46 m
ΔPE = 31.6536 J
Therefore, the change in gravitational potential energy of the shot is 31.6536 Joules.