Question

1)

Calculate the magnitude of the linear momentum for the following cases.

(a) a proton with mass 1.67  10^-27 kg, moving with a speed of 4.65  10⁶ m/s
kg · m/s

(b) a 17.5-g bullet moving with a speed of 340 m/s
kg · m/s

(c) a 73.5-kg sprinter running with a speed of 12.5 m/s
kg · m/s

(d) the Earth (mass = 5.98  10²⁴ kg) moving with an orbital speed equal to 2.98  10⁴ m/s.
kg · m/s

2)

A soccer player takes a corner kick, lofting a stationary ball 36.0° above the horizon at 17.0 m/s. If the soccer ball has a mass of 0.425 kg and the player's foot is in contact with it for 4.80 ✕ 10⁻² s, find the x- and y-components of the soccer ball's change in momentum and the magnitude of the average force exerted by the player's foot on the ball.

(a) the x- and y-components of the soccer ball's change in momentum (in kg · m/s)

Δpx= kg · m/s

Δp_y= kg · m/s

(b)the magnitude of the average force exerted by the player's foot on the ball (in N)

Answer 1

(1) Linear momentum of an object is defined as -

p = m*v

where, m = mass of the object

v = speed of the object

(a) m = 1.67 x 10^-27 kg

v = 4.65 x 10^6 m/s

So, linear momentum of the proton, p = (1.67 x 10^-27 x 4.65 x 10^6) kg*m/s

= 7.77 x 10^-21 kg*m/s (Answer)

(b) m = 17.5 g = 17.5 x 10^-3 kg

v = 340 m/s

So, linear momentum of the bullet, p = (17.5 x 10^-3 x 340) kg*m/s

= 5.95 kg*m/s (Answer)

(c) m = 73.5 kg

v = 12.5 m/s

So, linear momentum of the sprinter, p = (73.5 x 12.5) kg*m/s

= 918.75 kg*m/s (Answer)

(d) m = 5.98 x 10^24 kg

v = 2.98 x 10^4 m/s

So, linear momentum of the Earth, p = (5.98 x 10^24 x 2.98 x 10^4) kg*m/s

= 1.78 x 10^29 kg*m/s (Answer)