A shot-putter puts a shot (weight = 71.9 N) that leaves his hand at distance of 1.47 m above the ground.
(a) Find the work done by the gravitation force when the shot has risen to a height of 2.20 m above the ground. Include the correct sign for work.
J
(b) Determine the change (ÄPE = PEf - PE0) in the gravitational potential energy of the shot.
J
The shot rises against gravity for (2.20 - 1.47) = .73 m
therefore the work done which is negative because the force is down and the motion up = - m g (.73) = -71.9(.73) = -52.5 Joules
b. 52.5 Joules
comes out of kinetic energy and goes to potential energy
To find the work done by the gravitational force when the shot has risen to a height of 2.20 m above the ground, we need to calculate the change in potential energy (PE).
(a) Work done by the gravitational force is given by the equation W = -ΔPE, where W is the work done and ΔPE is the change in potential energy. Since the shot is moving against the gravitational force, the work is negative.
The formula for potential energy (PE) is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given that the weight (force due to gravity) of the shot is 71.9 N, we can calculate the mass using the formula m = F/g, where F is the weight and g is the acceleration due to gravity (approximately 9.8 m/s^2).
m = 71.9 N / 9.8 m/s^2 = 7.34 kg (rounded to two decimal places)
Now, let's calculate the initial potential energy (PE0) when the shot leaves the hand at a distance of 1.47 m above the ground.
PE0 = mgh0
= (7.34 kg)(9.8 m/s^2)(1.47 m)
= 105.68 J (rounded to two decimal places)
Next, we'll calculate the final potential energy (PEf) when the shot rises to a height of 2.20 m above the ground.
PEf = mghf
= (7.34 kg)(9.8 m/s^2)(2.20 m)
= 163.12 J (rounded to two decimal places)
Finally, we can find the work done (W) by the gravitational force.
W = -ΔPE
= -(PEf - PE0)
= -(163.12 J - 105.68 J)
= -57.44 J (rounded to two decimal places)
Therefore, the work done by the gravitational force is -57.44 J (with the negative sign indicating that work is done against gravity).
(b) To determine the change in gravitational potential energy (ΔPE), we simply subtract the initial potential energy (PE0) from the final potential energy (PEf).
ΔPE = PEf - PE0
= 163.12 J - 105.68 J
= 57.44 J
Therefore, the change in gravitational potential energy of the shot is 57.44 J.