A body of mass 3kg falls freely from rest through a height of 60m and comes to rest having penetrated 6.0 of sand calculate 1: velocity
2: time taking
3: average Force
To calculate the answers, we can use the principles of energy and motion equations. Here's how:
1: Velocity:
The initial potential energy of the body is converted into kinetic energy as it falls. Considering there is no air resistance, we can equate the potential energy to kinetic energy. The potential energy is given by mgh, where m is the mass (3kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height (60m).
Potential energy = mgh = 3kg * 9.8 m/s² * 60m = 1764 J
Since the body comes to rest after penetrating 6.0m of sand, we can assume all the kinetic energy has been dissipated. No potential energy remains. Thus, the final velocity is zero.
2: Time taken:
We can use the formula of motion equation s = ut + (1/2)at², where s is the distance (60m), u is the initial velocity (0 m/s), a is the acceleration (acceleration due to gravity, -9.8 m/s²), and t is the time taken.
Rearranging the equation, we can solve for time:
60m = (1/2)(-9.8 m/s²)t²
120m = (-9.8 m/s²)t²
t² = -120m / (-9.8 m/s²)
t² = 12.24 s²
t = √(12.24) s
t ≈ 3.5 s (approx)
3: Average Force:
The average force can be calculated using the impulse-momentum principle, which relates force and change in momentum. In this case, the change in momentum is equal to the impulse experienced by the body while penetrating the sand.
We can find the change in momentum using the equation p = mv, where p is momentum, m is mass (3kg), and v is velocity (initial velocity, which is zero).
Change in momentum = mv = 3kg * 0 m/s = 0 kg*m/s
Impulse is equal to the change in momentum, so impulse = 0 kg*m/s
The average force can be calculated by dividing the impulse by the time taken:
Average force = impulse / time = 0 kg*m/s / 3.5s
Average force ≈ 0 N (approx)
Therefore, the answers are:
1: Velocity = 0 m/s
2: Time taken ≈ 3.5 s (approx)
3: Average Force ≈ 0 N (approx)