A 8.6-kg rock and a 5.9 × 10-4-kg pebble are held near the surface of the earth. (a) Determine the magnitude of the gravitational force exerted on each by the earth. (b) Calculate the magnitude of the acceleration of each object when released.
For b), would the accelerations of both the rock and pebble be +9.8 m/s^2?
Please help, thanks!
To determine the magnitude of the gravitational force exerted on both the rock and pebble by the Earth, we can use the formula for gravitational force:
F = mg
Where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity, which is approximately 9.8 m/s^2 near the surface of the Earth.
For the rock:
m₁ = 8.6 kg
F₁ = m₁g = 8.6 kg × 9.8 m/s^2 = 84.28 N
For the pebble:
m₂ = 5.9 × 10^(-4) kg (Note: The mass is given in scientific notation)
F₂ = m₂g = 5.9 × 10^(-4) kg × 9.8 m/s^2 = 5.782 × 10^(-3) N
So the magnitude of the gravitational force exerted on the rock is 84.28 N, while the magnitude of the gravitational force exerted on the pebble is 5.782 × 10^(-3) N.
For part (b), when both objects are released, they will experience the same acceleration due to gravity, which is approximately +9.8 m/s^2 near the surface of the Earth. This means that their accelerations will be the same.
Therefore, the accelerations of both the rock and pebble will indeed be +9.8 m/s^2 when they are released.