Question

(A) Calculate the acceleration of gravity, gC, on Ceres Apply the kinematics displacement equation to the...

(A) Calculate the acceleration of gravity, gC, on Ceres

Apply the kinematics displacement equation to the falling rock.

(1)

Δx = 1/2at2 + v0t

Substitute Δx = -10.0 m, v0 = 0, a = -gC, and t = 8.06 s, and solve for the gravitational acceleration on Ceres, gC.

-10.0 m = -1/2gC(8.06 s)2 → gC = 0.308 m/s2

(B) Find the mass of Ceres.

Equate the weight of the rock on Ceres to the gravitational force acting on the rock.

mgC = G MCm
RC2

Solve for the mass of Ceres, MC.

MC = gCRC2 = 1.20  1021 kg
G

(C) Calculate the acceleration of gravity at a height of 50.0 km above the surface of Ceres.

Equate the weight at 50.0 km to the gravitational force.

mg'C = G mMC
r2

Cancel m, then substitute r = 5.60  105 m and the mass of Ceres.

g'C = G MC
r2
= (6.67  10-11 kg-1m3s-2) 1.20  1021 kg
(5.60  105 m)2

= 0.255 m/s2

PRACTICE IT

Use the worked example above to help you solve this problem. An astronaut standing on the surface of Ceres, the largest asteroid, drops a rock from a height of 10.0 m. It takes 8.06 s to hit the ground.

(a) Calculate the acceleration of gravity on Ceres.
m/s2

(b) Find the mass of Ceres, given that the radius of Ceres is RC = 5.10  102 km.
kg

(c) Calculate the gravitational acceleration 53.0 km from the surface of Ceres.
m/s2

EXERCISE

An object takes 2.95 s to fall 4.95 m on a certain planet.

(a) Find the acceleration due to gravity on the planet.
m/s2

(b) Find the planet's mass if its radius is 5250 km.
kg

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