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 4.00 106 m/s
(b) a 16.5 g bullet moving with a speed of 270 m/s
(c) a 70.5 kg sprinter running with a speed of 12.5 m/s
(d) the Earth (mass = 5.98 1024 kg) moving with an orbital speed equal to 2.98 104
If you want something to a power use the little up arrow, upper case 6. For example x^3 is x cubed.
a)
1.67 * 10^-27 * 4.00*10^6
=(1.67*4)* 10^-21
= 6.68 * 10^-21 kg m/s
all to three significant figures since 4.00 and 1.67 are three figures
b)
16.5 g * 10^-3 kg/g = 16.5 * 10^-3 kg = 1.65*10^-2 kg
270 m/s = 2.70*10^2
now do (1.65*2.70)* 10^-2 * 10^2
=4.455*10^0 but we want three significant figures and anything^0 = 1 so
4.46 kg m/s
To calculate the magnitude of the linear momentum, we need to use the formula:
Linear Momentum (p) = mass (m) × velocity (v)
where
- mass (m) is given in kilograms (kg)
- velocity (v) is given in meters per second (m/s)
Let's calculate the linear momentum for each case:
(a) Linear momentum of a proton:
mass (m) = 1.67 × 10^(-27) kg
velocity (v) = 4.00 × 10^6 m/s
p = m × v
p = (1.67 × 10^(-27) kg) × (4.00 × 10^6 m/s)
p = 6.68 × 10^(-21) kg⋅m/s
Therefore, the magnitude of the linear momentum for a proton is 6.68 × 10^(-21) kg⋅m/s.
(b) Linear momentum of a bullet:
mass (m) = 16.5 g = 0.0165 kg
velocity (v) = 270 m/s
p = m × v
p = (0.0165 kg) × (270 m/s)
p = 4.455 kg⋅m/s
Therefore, the magnitude of the linear momentum for a bullet is 4.455 kg⋅m/s.
(c) Linear momentum of a sprinter:
mass (m) = 70.5 kg
velocity (v) = 12.5 m/s
p = m × v
p = (70.5 kg) × (12.5 m/s)
p = 881.25 kg⋅m/s
Therefore, the magnitude of the linear momentum for a sprinter is 881.25 kg⋅m/s.
(d) Linear momentum of the Earth:
mass (m) = 5.98 × 10^24 kg
velocity (v) = 2.98 × 10^4 m/s
p = m × v
p = (5.98 × 10^24 kg) × (2.98 × 10^4 m/s)
p = 1.78044 × 10^29 kg⋅m/s
Therefore, the magnitude of the linear momentum for the Earth is 1.78044 × 10^29 kg⋅m/s.
To calculate the magnitude of linear momentum, you can use the formula:
Linear momentum (p) = mass (m) × velocity (v)
Let's calculate the magnitude of linear momentum for each case:
(a) Proton:
Mass (m) = 1.67 × 10^(-27) kg
Velocity (v) = 4.00 × 10^6 m/s
To find the magnitude of linear momentum (p), multiply the mass and velocity:
p = m × v = 1.67 × 10^(-27) kg × 4.00 × 10^6 m/s
(b) Bullet:
Mass (m) = 16.5 g = 16.5 × 10^(-3) kg
Velocity (v) = 270 m/s
To find the magnitude of linear momentum (p), multiply the mass and velocity:
p = m × v = 16.5 × 10^(-3) kg × 270 m/s
(c) Sprinter:
Mass (m) = 70.5 kg
Velocity (v) = 12.5 m/s
To find the magnitude of linear momentum (p), multiply the mass and velocity:
p = m × v = 70.5 kg × 12.5 m/s
(d) Earth:
Mass (m) = 5.98 × 10^24 kg
Velocity (v) = 2.98 × 10^4 m/s
To find the magnitude of linear momentum (p), multiply the mass and velocity:
p = m × v = 5.98 × 10^24 kg × 2.98 × 10^4 m/s
Once you calculate the products of mass and velocity for each case, you will have the respective magnitudes of linear momentum.