(a) What is the force on the tree?
(b) What is the effective force exerted by the end of the tip of the root to keep the tree from toppling?
(c) What could you have done to ensure that the tree does not uproot easily?
To calculate the force on the tree, we can use the impulse-momentum theorem. The initial momentum of the ball is zero, and after the collision, it is 2.5 kg⋅m/s downward. With a collision time of 10 ms, the average force applied to the tree is 250 N.
To calculate the effective force exerted by the tip of the root to prevent toppling, we need to consider the torque due to the weight of the tree and the applied force. The torque due to the weight of the tree is 741 N⋅m, and the effective force at the tip of the root to keep the tree from toppling is 3705 N.
To ensure that the tree does not uproot easily, you can plant the tree in a deep and wide hole, stake it with guy wires, select a suitable species for the climate, soil conditions, sunlight, water, and nutrients, and prune it regularly.
The force on the tree
The force on a palm tree struck by a ball is 250 N. This force is calculated using the impulse-momentum theorem, which considers the change in momentum of the ball during the collision.
The ball hits the top of the tree with a speed of 5 m/s and stays in contact with it for 10 ms. The change in momentum of the ball is 2.5 kg⋅m/s downward. Dividing this by the collision time gives an average force of 250 N applied to the tree.
To calculate the effective force exerted by the tip of the root to prevent toppling, we need to consider the torque on the tree due to its weight and the applied force. The torque due to the weight of the tree is 741 N⋅m, and the effective force at the tip of the root to keep the tree from toppling is 3705 N.
What could you have done to ensure that the tree does not uproot easily?
1. Plant the tree in a deep and wide hole to provide better support for the root system.
2. Backfill the hole with compacted soil.
3. Stake the tree with guy wires anchored to the ground for additional support.
4. Select a palm tree species suitable for the local climate and soil conditions.
5. Ensure the tree receives adequate sunlight, water, and nutrients.
6. Prune the tree regularly to maintain its health and stability.
By following these steps, you can help ensure that your palm tree remains stable and healthy for a long time.