A bullet with a mass of 7.11 g and a speed
of 774 m/s penetrates a tree horizontally to
a depth of 1.85 cm. Assume that a constant
frictional force stops the bullet.
Calculate the magnitude of this frictional
force. Try energy considerations.
Answer in units of N
To calculate the magnitude of the frictional force, we can use the principle of conservation of mechanical energy. The bullet loses its kinetic energy as it penetrates the tree due to the work done by the frictional force.
First, we need to find the initial kinetic energy (KEi) of the bullet. The formula for kinetic energy is:
KE = (1/2) * m * v^2
where m is the mass of the bullet and v is its velocity.
Substituting the given values:
m = 7.11 g = 0.00711 kg
v = 774 m/s
KEi = (1/2) * 0.00711 kg * (774 m/s)^2
Next, we need to find the final kinetic energy (KEf) of the bullet. Since the bullet comes to a stop, its final kinetic energy will be zero.
Using the formula for work (W), which is equal to the force (F) multiplied by the distance (d) traveled:
W = F * d
The work done by the frictional force is equal to the change in kinetic energy:
W = KEi - KEf
Since KEf is zero, the work done by the frictional force becomes:
W = KEi - 0
W = KEi
Equating this with F * d:
F * d = KEi
Rearranging the equation, we can solve for F:
F = KEi / d
Substituting the values:
KEi = 0.5 * 0.00711 kg * (774 m/s)^2
d = 0.0185 m
F = (0.5 * 0.00711 kg * (774 m/s)^2) / 0.0185 m
Calculate the expression and round the result to the appropriate number of significant figures to obtain the magnitude of the frictional force in newtons (N).