Question

A player hits a football which is initially at rest and moves 22 m/s.
Find the:

a. momentum of the football if it has a mass of 0.48 kg
b. force exerted on it when the time of contact is 0.03s
c. impulse in the football

Answer 1

Answer on Question 58026, Physics, Mechanics, Relativity

Question:

A player hits a football which is initially at rest and moves $22 \, ms^{-1}$.

Find the:

a) momentum of the football if it has a mass of $0.48 \, kg$

b) force exerted on it when the time of contact is $0.03 \, s$

c) impulse in the football

Solution:

a) By definition of the momentum, we have:

$$p = m v = 0.48 \, kg \cdot 22 \, ms^{-1} = 10.56 \, kg \, ms^{-1}.$$

b) Because the force is the rate of change of momentum, we get:

$$F \Delta t = \Delta p,$$ $$F = \frac{\Delta p}{\Delta t} = \frac{m(v - v_0)}{\Delta t} = \frac{0.48 \, kg \cdot (22 \, ms^{-1} - 0 \, ms^{-1})}{0.03 \, s} = 352 \, N.$$

c) By definition of the impulse, we have:

$$\begin{array}{l} J = \Delta p = p - p_0 = m v - m v_0 = m(v - v_0) = 0.48 \, kg \cdot (22 \, ms^{-1} - 0 \, ms^{-1}) = \\ = 10.56 \, kg \, ms^{-1}. \end{array}$$

Answer:

a) $p = 10.56 \, kg \, ms^{-1}$.

b) $F = 352 \, N$.

c) $J = 10.56 \, kg \, ms^{-1}$.

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