Pluto has a mass of 1.30 1022 kg and a radius of 1.18 106 m
(a) What is the acceleration due to gravity on Pluto?
(b) How much would a 4.7-kg person weigh on this planet?
a) GMp/r^2
b) GMp*4.7/r^2
To find the acceleration due to gravity on Pluto, you can use the formula:
acceleration due to gravity (g) = (gravitational constant * mass of Pluto) / (radius of Pluto)^2
(a) The gravitational constant is a constant value represented by G = 6.67430 x 10^-11 N(m/kg)^2.
Plugging in the values for mass and radius of Pluto:
g = (6.67430 x 10^-11 N(m/kg)^2 * 1.30 x 10^22 kg) / (1.18 x 10^6 m)^2
Simplifying the equation:
g = (6.67430 x 10^-11 N(m/kg)^2 * 1.30 x 10^22 kg) / (1.39 x 10^12 m^2)
Calculating the acceleration due to gravity on Pluto:
g ≈ 0.6206 m/s^2
Therefore, the acceleration due to gravity on Pluto is approximately 0.6206 m/s^2.
(b) To determine how much a 4.7-kg person would weigh on Pluto, you can use the formula:
Weight (W) = mass (m) * acceleration due to gravity (g)
Plugging in the values:
W = 4.7 kg * 0.6206 m/s^2
Calculating the weight of the person on Pluto:
W ≈ 2.9182 N
Therefore, a 4.7-kg person would weigh approximately 2.9182 Newtons on Pluto.
To find the acceleration due to gravity and the weight of a person on Pluto, we can use the following formulas:
(a) The acceleration due to gravity (g) can be calculated using the formula:
g = G * (M / r^2)
where:
G is the universal gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M is the mass of Pluto (1.30 × 10^22 kg)
r is the radius of Pluto (1.18 × 10^6 m)
(b) The weight of a person can be calculated using the formula:
Weight = mass * g
where:
mass is the mass of the person (4.7 kg)
g is the acceleration due to gravity on Pluto (from part a)
Let's calculate these step-by-step:
(a) Calculating the acceleration due to gravity on Pluto:
Step 1: Substitute the given values into the formula:
g = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (1.30 × 10^22 kg) / (1.18 × 10^6 m)^2
Step 2: Simplify the equation inside the brackets:
g = (6.67430 × 1.30 × 10^22 kg * 10^-11 m^3 kg^-1 s^-2) / (1.18 × 10^6 m)^2
Step 3: Solve the equation:
g = (8.674790000000001 × 10^11 m^3 kg^-1 s^-2) / (1.3924 × 10^12 m^2)
Step 4: Simplify the units and divide:
g = 6.218 m/s^2
(b) Calculating the weight of a 4.7-kg person on Pluto:
Step 5: Substitute the mass of the person and the acceleration due to gravity into the formula:
Weight = 4.7 kg * 6.218 m/s^2
Step 6: Calculate the weight:
Weight = 29.1826 N
Therefore,
(a) The acceleration due to gravity on Pluto is approximately 6.218 m/s^2.
(b) A 4.7-kg person would weigh approximately 29.1826 Newtons on Pluto.