Circular Motion & Gravity Worksheet Questions

The cylindrical tub of a washing machine has a radius of 34 cm. During the spin cycle, the wall of the tub rotates with a tangential speed of 5.6 m/s. Calculate the centripetal acceleration of the clothes sitting against the tub.

Ac = 89 m/s^2

You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 s. How tall is the tower?

L = 36 m

what is the period of a 3.98 m long pendulum? what is the period of a 99.4 cm long pendulum?

T = 4.00 s T = 2.00 s

During the spacecraft's fifth orbit around Venus, Magellan traveled at a mean altitude of 361 km. If the orbit had been circular, what would Magellan's period and speed have been?

T = 5.66 x 10^3 s Vf = 7.12 x 10^3 m/s

A test car moves at a constant speed around a circular path. If the car is 48.2 m from the track's center and has a centripetal acceleration of 8.05 m/s^2, what is the car's tangential speed?

Vt = 19.7 m/s

A spring constant 30.0 N/m is attached to different masses, and the system is set in motion. Find the period and frequency of vibration for masses of the following magnitudes: a. 2.3 kg b. 15 g c. 1.9 kg

a. T = 1.7 s & F = 0.6 Hz b. T = 0.14 s & F = 7.1 Hz c. T = 1.6 s & F = 0.6 Hz

What is the free fall acceleration at a location where a 6.00 m long pendulum swings through exactly 100 cycles in 492 s?

ag = 9.79 m/s^2

Find the gravitational force that earth ( mass = 5.97 x 10^24 kg) exerts on the moon (mass = 7.35 x 10^22 kg) when the distance between them is 3.84 x 10^8 m

fg = 1.99 x 10^20 N

A body of a 1275 kg car is supported on a frame of four springs. Two people riding in the car have a combining mass of 153 kg. When driven over a pothole in the road, the frame vibrates with a period of 0.840 s. For the first few seconds, the vibration approximates simple harmonic motion. Find the spring constant of a single spring.

k = 2.00 x 10^4 N/m

If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?

k = 270 N/m

A 1.0 kg mass attached to one end of a spring completes one oscillation every 2.0 s. Find the spring constant.

k = 9.9 N/m

A desktop toy pendulum swings back and forth once every 1.0 s. How long is this pendulum?

l = 0.25 m

a spring of k = 1962 N/m loses its elasticity if stretched more than 50.0 cm. What is the mass of the heaviest object the spring can support without being damaged?

m = 1.00 x 10^2 kg

A pilot is flying a small plane at 56.6 m/s in a circular path with a radius of 188.5 m. The centripetal force needed to maintain the planes circular motion is 1.89 x 10^ 4 N. What is the planes mass?

m = 1.11 x 10^3 kg

A large planet orbiting a distant star is discovered. The planet's orbit is nearly circular and fairly close to the star. The planet's orbital distance is 7.50 x 10^10 m, and its period is 105.5 days. Calculate the mass of the star.

m = 3.00 x 10^30 kg

Tarzan tries to cross a river by swinging from one bank to another on a vine that is 10.o m long. His speed at the bottom of the swing is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 x 10^3 N. What is the largest mass that Tarzan can have and still make it safely across the river?

m = 62 kg

Find the distance between a 0.300 kg billiard ball and a 0.400 kg billiard ball of the magnitude of the gravitational force between them is 8.92 x 10^-11 N.

r = 3.00 x 10^-1 m

A 76 N crate hung from a spring (k = 450 N/m) How much displacement is caused by the weight of the crate?

x = -0.17 m