A body of mass 20kg falls from rest through a height of 10m and comes to rest having penerated a distance of 9.8m into sandy ground calculate the average force exerted by the sand in bringing the body to rest(take g=10m/s^2)
get crash speed
(1/2) m v^2 = m g h
v = sqrt (2 g h) (but you knew that, right?)
v = sqrt (2*9.81*10) = 14 meters/second
momentum at crash = m v = 20 * 14 = 280 kg m/s
calculate time to stop
average stop speed = 7 m/s
stop distance = 9.8 meters
t = stop time = 9.8 m / 7 m/s = 1.4 seconds
average force = change of momentum / time to stop = 280 /1.4 = 200 Newtons
To calculate the average force exerted by the sand in bringing the body to rest, you can use the concept of work and energy.
1. First, calculate the potential energy of the body when it falls through a height of 10m. The formula for potential energy is given by:
Potential Energy = mass × gravity × height
Potential Energy = 20kg × 10m/s² × 10m
Potential Energy = 2000 Joules
2. Next, calculate the work done by the sand in stopping the body. The work done is equal to the change in mechanical energy, which is the difference between the initial potential energy and the final kinetic energy.
Work Done = Change in Mechanical Energy
Work Done = Final Kinetic Energy - Initial Potential Energy
Since the body comes to rest, the final kinetic energy is zero. Therefore:
Work Done = 0 - 2000 Joules
Work Done = -2000 Joules
3. Finally, calculate the average force exerted by the sand using the work-energy principle:
Average Force = Work Done / Distance
Average Force = -2000 Joules / 9.8m
Average Force ≈ -204.08 Newtons
Note: The negative sign indicates that the average force exerted by the sand is in the opposite direction of the body's displacement.
To calculate the average force exerted by the sand in bringing the body to rest, we need to use the principles of work and energy.
Here's how we can calculate it step by step:
Step 1: Calculate the gravitational potential energy (PE) of the body when it falls through a height of 10m.
Gravitational potential energy is given by the formula:
PE = m * g * h
where m is the mass of the body, g is the acceleration due to gravity, and h is the height.
Given:
Mass (m) = 20 kg
Height (h) = 10 m
Acceleration due to gravity (g) = 10 m/s^2
PE = 20 kg * 10 m/s^2 * 10 m
PE = 2000 J
Step 2: Calculate the work done by the sand in stopping the body.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
Initially, the body is at rest, so the initial kinetic energy (KEi) is zero.
Finally, the body comes to rest after penetrating the ground by a distance of 9.8m. At this point, the final kinetic energy (KEf) is also zero.
Therefore, the work done by the sand (W) is equal to the change in kinetic energy:
W = KEf - KEi
Since both KEf and KEi are zero, the work done by the sand is also zero.
Step 3: Calculate the average force exerted by the sand.
The average force (F) can be calculated using the work-energy principle formula:
W = F * d
where F is the force, and d is the distance over which the force is applied.
Given that W = 0 (from Step 2), we have:
0 = F * 9.8 m
Therefore, the average force exerted by the sand in bringing the body to rest is zero.
Explanation: Since the final kinetic energy of the body is zero, it means that all its initial gravitational potential energy was fully converted into work done against the sand's resistance, resulting in the body coming to rest. However, since the body has come to rest, the average force exerted by the sand is zero.