An engineer at NASA is investigating the impact of meteorites on planets. He performs experiments in a vacuum by dropping metal spheres of different sizes and different heights above a horizontal bed of sand. In one experiment, a metal sphere of mass 0.1 kg is dropped from a height of 1.2 m. The sphere makes a depression in the sand of 2 cm.
[Gravitational field strength, g = 10 Nkg -1 ]
i) Calculate the potential energy of the sphere at a height of 1.2 m [2 marks] ______________________________________________ ______________________________________________
ii) Calculate the work done by the sphere as it comes to rest in the sand [2 marks].
i) Well, to calculate the potential energy of the sphere, we can use a simple formula: Potential Energy = mass x gravity x height. Since we know the mass of the sphere is 0.1 kg, the height is 1.2 m, and the gravitational field strength is 10 N/kg, we can plug these values into the formula and get: Potential Energy = 0.1 kg x 10 N/kg x 1.2 m = 1.2 joules.
ii) Now let's calculate the work done by the sphere as it comes to rest in the sand. The work done can be calculated using the formula: Work done = force x distance. In this case, the force is the weight of the sphere, which is given by the formula: Weight = mass x gravity. So, the weight of the sphere is 0.1 kg x 10 N/kg = 1 N. Now, let's find the distance the sphere has traveled. Since it made a depression in the sand of 2 cm, which is equivalent to 0.02 m, we can say that the distance traveled is 0.02 m. So, let's calculate the work done: Work done = force x distance = 1 N x 0.02 m = 0.02 joules. Voila! Hope that helps, and keep those meteorites in check!
i) To calculate the potential energy of the sphere, we will use the formula:
Potential energy = mass x gravitational field strength x height
Given:
mass (m) = 0.1 kg
gravitational field strength (g) = 10 N/kg
height (h) = 1.2 m
Substituting these values, we can calculate the potential energy:
Potential energy = 0.1 kg x 10 N/kg x 1.2 m
Potential energy = 1.2 J
Therefore, the potential energy of the sphere at a height of 1.2 m is 1.2 Joules.
ii) The work done by the sphere as it comes to rest in the sand is equal to the potential energy lost by the sphere.
From part i, we know that the potential energy at a height of 1.2 m is 1.2 J.
As the sphere comes to rest, this potential energy is converted into the energy required to make the depression in the sand. In this case, the depression is 2 cm or 0.02 m.
Therefore, the work done by the sphere is:
Work done = Potential energy lost = 1.2 J
So, the work done by the sphere as it comes to rest in the sand is 1.2 Joules.
i) To calculate the potential energy of the sphere at a height of 1.2 m, we can use the formula:
Potential energy (PE) = mass (m) x gravitational field strength (g) x height (h)
Given that the mass of the sphere is 0.1 kg, the gravitational field strength is 10 N/kg, and the height is 1.2 m, we can substitute these values into the formula:
PE = 0.1 kg x 10 N/kg x 1.2 m
PE = 1.2 Joules
Therefore, the potential energy of the sphere at a height of 1.2 m is 1.2 Joules.
ii) The work done by the sphere as it comes to rest in the sand can be calculated using the formula:
Work done (W) = force (F) x distance (d)
Since the sphere makes a depression in the sand of 2 cm, which is equivalent to 0.02 m, we can use this value as the distance.
The force can be calculated using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the acceleration is the acceleration due to gravity, which is the same as the gravitational field strength, g.
So, the force can be calculated as:
F = mass (m) x acceleration (g)
F = 0.1 kg x 10 N/kg
F = 1 N
Now, we can substitute the force and distance values into the formula for work done:
W = 1 N x 0.02 m
W = 0.02 Joules
Therefore, the work done by the sphere as it comes to rest in the sand is 0.02 Joules.