A 48.0 kg child is stationary in the middle of an ice rink (no friction). A 0.750 kg football is thrown with a velocity of 21.2 m/s moving eastward. The child catches the ball and together they slide off in the eastward direction with a velocity of 0.326 m/s. Take east to be positive.
a) Find the impulse (magnitude and direction) experienced by the football during the collision.
b) Find the impulse (magnitude and direction) experienced by the child during the collision.
c) Suppose the collision lasted 0.254 sec. Find the average force (magnitude and direction) experienced by the child during the collision.
d) What was the child’s average acceleration during the collision?
e) Characterize the collision as elastic, inelastic, or completely inelastic
What is your question about this? It appears straightforward.
a. impulse = change momentum
initial momentumball=finalmomentumball+finalmomentum child
.75*21.1=(.75+48)velocityfinal
solve for velocity fnal, then determine the momentum change of the ball, and the child.
c. force*time=changemomentum
To solve this problem, we will use the principles of conservation of momentum and impulse.
a) The impulse experienced by an object can be calculated using the equation:
Impulse = Change in momentum
The initial momentum of the football is given by:
Momentum_initial = mass * velocity_initial
Momentum_initial = 0.750 kg * 21.2 m/s (east)
The final momentum of the football can be calculated by using the fact that the child and the football slide off together, so their combined momentum must be zero:
Momentum_final = (mass_child + mass_football) * velocity_final
Momentum_final = (48.0 kg + 0.750 kg) * 0.326 m/s (east)
Change in momentum = Momentum_final - Momentum_initial
The magnitude of impulse can be found using the equation Impulse = change in momentum:
Impulse = |Change in momentum|
The direction of the impulse can be determined by the direction of the change in momentum (east or west).
b) Similar to part (a), the impulse experienced by the child can be found using the equation Impulse = Change in momentum. The initial momentum of the child is zero since they are stationary. The change in momentum is equal to the momentum final of the child, which will be in the eastward direction (positive).
c) The average force experienced by an object during a collision can be calculated using the equation:
Average Force = Impulse / Time
We have already calculated the impulse in part (b). The given time is 0.254 sec.
d) The average acceleration experienced by an object during a collision can be calculated using the equation:
Average Acceleration = Change in velocity / Time
The change in velocity is the final velocity minus the initial velocity. In this case, the child's initial velocity is zero, and the final velocity is given as 0.326 m/s east. The given time is 0.254 sec.
e) To characterize the collision as elastic, inelastic, or completely inelastic, we can examine the effect of the collision on the kinetic energy. If the kinetic energy is conserved, the collision is elastic. If the kinetic energy decreases, the collision is inelastic. If the objects stick together after the collision, the collision is completely inelastic.
To determine this, we can compare the initial kinetic energy with the final kinetic energy. The initial kinetic energy of the football and the child can be calculated using the equation:
Initial Kinetic Energy = (1/2) * mass * (velocity^2)
The final kinetic energy can be calculated using the same equation, where the mass is the combined mass of the child and the football, and the velocity is the final velocity after the collision.
By comparing these two kinetic energies, we can determine the nature of the collision.