Question

A 52.0-kg sandbag falls off a rooftop that is 22.0 m above the ground. The collision between the sandbag and the ground lasts for a total of 17.0 ms. What is the magnitude of the average force exerted on the sandbag by the ground during the collision?

I don't even know where to start... what formulas should I be using?

Answer 1

This question requires using the impulse equation:

where the impulse I is equal to the force F exerted on an object over a period of time for a mass m that undergoes a change in velocity .

It also requires the kinematic equation:

with the final velocity v_f, initial velocity v₀, acceleration a, and distance d.

Step 1) Since they want the force that the ground exerts on the bag as it hits, the impulse equation is needed, given that has the force in it in terms of the other available variables:

Step 2) Solve for the force F:

Step 3) Given that the mass and the interval of time are both given, all that's left is to get the change in velocity, so that the force can be determined. The change in velocity will come from the velocity of the sandbag just before it hits the ground, to it finishing coming to rest after hitting the ground. So the change in velocity of the sandbag will then just be equal to the velocity of it just before it hits the ground (since the final velocity after hitting the ground is zero). Therefore, the kinematic equation is needed:

Step 4) Given that the bag is starting from rest, the initial velocity v₀ there is just 0:

Step 5) And the acceleration of the sandbag as it is falling is just the acceleration due to gravity g:

Step 6) And solve that for the final velocity v_f:

Step 7) Substitute that in for the change in velocity from step 2:

Step 8) With the expression for the force now known, just fill in 52.0 kg for the mass m, 9.8m/s² for g, 22.0 m for the distance d that the sandbag falls, and 0.017s (the 17.0 ms) for the change in time that it takes the bag to stop after hitting the ground:

So the force exerted on the bag as it hits the ground is about 63,500 N, or 63.5 kN.