A 0.60-kg basketball is dropped out of the window that is 6.1 m above the ground. The ball is caught by a person whose hands are 1.2 m above the ground.
(a) How much work is done on the ball by its weight?
(b) What is the gravitational potential energy of the basketball, relative to the ground when it is released?
(c)What is the gravitational potential energy of the basketball when it is caught?
(d) How is the change (PEf - PE0) in the ball's gravitational potential energy related to the work done by its weight?
a. m*g = 0.6 * 9.8 = 5.88 N. = Wt. of the ball.
Work = F*d = 5.88 * (6.1-1.2) = 28.8 J.
b. PE = mg*h = 5.88 * 6.1 = 35.87 J.
c. PE = mg*h = 5.88 * 1.2 = 7.06 J.
d. (PEo-PEf) = 35.87 - 7.06 = 28.81 J. =
The work done on the ball.
a) The work done on the ball by its weight can be given by the formula: Work = Force x Distance. The force acting on the ball is its weight, which can be calculated using the formula: Weight = mass x gravity. The distance the ball falls is 6.1 m. So, the work done is:
Work = Weight x Distance
= (mass x gravity) x Distance
= (0.60 kg x 9.8 m/s^2) x 6.1 m
= 35.784 J (Joules)
Therefore, the work done on the ball by its weight is 35.784 Joules.
b) The gravitational potential energy of the basketball, relative to the ground when it is released, can be calculated using the formula: Potential Energy = mass x gravity x height. The mass of the basketball is 0.60 kg, the height is 6.1 m, and the gravity is 9.8 m/s^2. So,
Potential Energy = 0.60 kg x 9.8 m/s^2 x 6.1 m
= 35.784 J (Joules)
Therefore, the gravitational potential energy of the basketball, relative to the ground when it is released, is 35.784 Joules.
c) When the ball is caught by a person whose hands are 1.2 m above the ground, the gravitational potential energy of the basketball can be calculated using the same formula as in part b, but now the height is 1.2 m. So,
Potential Energy = 0.60 kg x 9.8 m/s^2 x 1.2 m
= 7.056 J (Joules)
Therefore, the gravitational potential energy of the basketball when it is caught is 7.056 Joules.
d) The change in gravitational potential energy (PEf - PE0) is equal to the work done by the weight of the ball. So, in this case,
Change in Potential Energy = Work Done
= 35.784 J (Joules)
The change in gravitational potential energy of the ball is equal to the work done by its weight, which is 35.784 Joules.
To solve this problem, we need to use the formulas for work and gravitational potential energy. Let's go step by step:
(a) The work done on an object by its weight is given by the formula:
Work (W) = Force (F) x Distance (d)
The weight of the basketball is given by the formula:
Weight (W) = mass (m) x gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
Plugging in the values:
Weight (W) = 0.60 kg x 9.8 m/s^2
Now, we can calculate the work done by the weight of the ball:
Work (W) = Weight (W) x Distance (d)
Note: The distance is the height of the window, which is 6.1 m.
Work (W) = (0.60 kg x 9.8 m/s^2) x 6.1 m
Calculate the result to get the work done on the ball by its weight.
(b) The gravitational potential energy of an object near the ground is given by the formula:
Potential Energy (PE) = mass (m) x gravity (g) x height (h)
The mass of the basketball is 0.60 kg, and the height is 6.1 m.
Plug these values into the formula to calculate the gravitational potential energy of the basketball when it is released.
(c) The gravitational potential energy of the basketball when it is caught can be calculated using the same formula as in part (b).
However, now the height is 1.2 m (the height of the person's hands).
Calculate the gravitational potential energy of the basketball when it is caught.
(d) The change in gravitational potential energy, (PEf - PE0), is related to the work done by its weight. According to the work-energy theorem, the work done by gravity equals the change in potential energy:
Work (W) = PEf - PE0
Rearrange the equation to solve for the change (PEf - PE0).
These steps should help you solve the problem. Let me know if you need any further assistance.
To answer these questions, we need to understand the concepts of work and gravitational potential energy.
(a) Work is defined as the product of force and displacement in the direction of the force. In this case, the only force acting on the basketball is its weight, which is given by the equation W = m * g, where W is the weight, m is the mass of the basketball, and g is the acceleration due to gravity.
To calculate work, we need to find the distance the ball travels. The ball is dropped from a height of 6.1 m and caught at a height of 1.2 m. So, the distance it falls is the difference between these two heights: 6.1 m - 1.2 m = 4.9 m.
Now, we can calculate work using the formula W = m * g * d, where d is the distance. Here, m = 0.60 kg and g = 9.8 m/s² (acceleration due to gravity):
W = 0.60 kg * 9.8 m/s² * 4.9 m = 28.392 J (joules)
Therefore, the work done on the ball by its weight is 28.392 J.
(b) Gravitational potential energy (PE) is the energy possessed by an object due to its position relative to other objects. The gravitational potential energy of an object near the surface of Earth is given by the equation PE = m * g * h, where h is the height of the object above a reference point.
When the basketball is released, its height above the ground is 6.1 m. So, we can calculate the gravitational potential energy relative to the ground:
PE = 0.60 kg * 9.8 m/s² * 6.1 m = 35.676 J
Therefore, the gravitational potential energy of the basketball, relative to the ground when it is released, is 35.676 J.
(c) When the basketball is caught, its height above the ground is 1.2 m. So, we can calculate the gravitational potential energy relative to the ground at this height using the same formula:
PE = 0.60 kg * 9.8 m/s² * 1.2 m = 7.056 J
Therefore, the gravitational potential energy of the basketball when it is caught is 7.056 J.
(d) The change in gravitational potential energy (PEf - PE0) is related to the work done by the weight of the basketball. In this case, the change in gravitational potential energy is the difference between the initial and final gravitational potential energies:
Change in PE = PEf - PE0
From parts (b) and (c), we know that PEf = 7.056 J and PE0 = 35.676 J. Substituting these values, we get:
Change in PE = 7.056 J - 35.676 J = -28.620 J
The negative sign indicates that the gravitational potential energy of the ball has decreased. This change in gravitational potential energy is equal to the work done by the weight of the ball, which we calculated as 28.392 J in part (a).
Therefore, the change (PEf - PE0) in the ball's gravitational potential energy is related to the work done by its weight, with the negative sign indicating a decrease in potential energy.