a 2.1 gram bullet is shot into a tree stump. Just before it hits the stump the bullet is moving at 280 m/s. The bullet penetrates into the tree and comes to a rest after having gone 5.1 cm into the tree
a.What was the initial kinetic energy of the bullet
b.What is the final kinetic energy of the bullet
c.How much work was done on the tree
d.what was the average force during the impact
a, b.
KE = (1/2)m*V^2
c.
The work done is the change in kinetic energy.
d.
W = F*d
a. To find the initial kinetic energy of the bullet, we can use the formula for kinetic energy:
Kinetic energy (KE) = 0.5 * mass * velocity^2
Substituting the given values into the formula:
KE = 0.5 * 2.1 g * (280 m/s)^2
= 0.5 * 0.0021 kg * (280 m/s)^2
= 0.5 * 0.0021 kg * 78400 m^2/s^2
= 82.32 J
Therefore, the initial kinetic energy of the bullet is 82.32 Joules.
b. To find the final kinetic energy of the bullet, we need to know the bullet's final velocity. Since the bullet comes to a rest after penetrating the tree, its final velocity is 0 m/s.
Kinetic energy (KE) = 0.5 * mass * velocity^2
Using the given values:
KE = 0.5 * 2.1 g * (0 m/s)^2
= 0 Joules
Therefore, the final kinetic energy of the bullet is 0 Joules.
c. The work done on the tree can be calculated using the work-energy principle. The work done (W) is equal to the change in kinetic energy of the bullet:
W = KE_initial - KE_final
= 82.32 J - 0 J
= 82.32 J
Therefore, the work done on the tree is 82.32 Joules.
d. The average force during the impact can be calculated using the work-energy principle. The work done (W) is equal to the force applied (F) times the distance the force is applied (d):
W = F * d
Rearranging the formula:
F = W / d
Using the values we have:
F = 82.32 J / 0.051 m
= 1616 N
Therefore, the average force during the impact is 1616 Newtons.
To find the answers to these questions, we need to use the principle of conservation of mechanical energy and the work-energy theorem.
Before we begin, it is important to note that the masses should be converted to kilograms before performing any calculations. Therefore, the mass of the bullet is 0.0021 kg.
a. To find the initial kinetic energy of the bullet, we can use the formula:
Initial Kinetic Energy = (1/2) * mass * velocity^2
Plugging in the values, we have:
Initial Kinetic Energy = (1/2) * 0.0021 kg * (280 m/s)^2
Calculating this, you will find the answer to be the initial kinetic energy of the bullet.
b. To find the final kinetic energy of the bullet, we can use the formula:
Final Kinetic Energy = (1/2) * mass * (final velocity)^2
Since the bullet comes to a rest, the final velocity would be zero:
Final Kinetic Energy = (1/2) * 0.0021 kg * 0^2
This would result in a final kinetic energy of zero.
c. To find the work done on the tree, we can use the formula:
Work = Force * Distance
Since the bullet penetrates into the tree, we can calculate the work done by knowing the distance the bullet traveled. The given distance is 5.1 cm, which can be converted to 0.051 meters.
Work = Force * 0.051 m
We can equate the work done to the change in kinetic energy of the bullet:
Work = Change in Kinetic Energy
Therefore:
Force * 0.051 m = Final Kinetic Energy - Initial Kinetic Energy
Substituting the known values, we can find the work done on the tree.
d. To find the average force during the impact, we can use the formula:
Average Force = Work / Distance
Since we have already calculated the work done in part c, we can divide that by the given distance of penetration (0.051 meters) to obtain the average force during impact.
By following these steps, you can find the answers to each question.