Q: A planet has an equatorial radius $$R = 4.50 \times 10^6$\ \mathrm{m}$$ and rotates once every $$12.0\ \mathrm{h}. $$What is the angular speed $$\omega of $$the planet?

$$1.45 \times 10$$^{-4}$$\ \mathrm{rad/s}$$

Question 1

A 1000 kg safe is connected by a rope over a frictionless pulley to a 500 kg piece of furniture on the floor. The coefficient of kinetic friction between the furniture and the floor is 0.50. If the safe is dropped 3.0 m, what is the acceleration of the system? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$3.3\ \mathrm{m/s^2$}$$

Question 2

What is the speed of the 1000 kg safe when it hits the truck 3.0 m below, assuming the acceleration found previously? (Use $$v^2$$ = $$v_0^2 + 2a$$\Delta y$$.)

Accepted Answer

$$5.4\ \mathrm{m/s}$$

Question 3

True or False: If the rope is massless and the pulley is frictionless, the tension is the same throughout the rope.

Accepted Answer

True

Question 4

Which of the following best describes the direction of the friction force acting on the 500 kg furniture?

Accepted Answer

Opposite to the direction of the furniture's motion

Question 5

A gibbon of mass $$9.0\ \mathrm{kg}$$ swings from a branch with an arm length of $$0.60\ \mathrm{m}$$ and a speed of $$3.5\ \mathrm{m/s} at $$the lowest point. What is the magnitude of the centripetal acceleration?

Accepted Answer

$$20.4\ \mathrm{m/s^2$}$$

Question 6

At the lowest point of the swing, the upward force provided by the branch must be:

Accepted Answer

Greater than the gibbon's weight

Question 7

What upward force must the branch provide to support the swinging gibbon at the lowest point?

Accepted Answer

$$358.2\ \mathrm{N}$$

Question 8

A planet has an equatorial radius $$R = 4.50 	imes 10^6$\ \mathrm{m}$$ and rotates once every $$12.0\ \mathrm{h}. $$What is the angular speed $$\omega of $$the planet?

Accepted Answer

$$1.45 	imes 10$$^{-4}$$\ \mathrm{rad/s}$$

Question 9

Which pair correctly gives the rover’s tangential speed and centripetal acceleration at the planet’s equator?

Accepted Answer

$$654.5\ \mathrm{m/s},\ 0.0952\ \mathrm{m/s^2$}$$

Question 10

True or False: The angular velocity vector of a rotating planet points along the planet’s axis of rotation.

Accepted Answer

True

Question 11

If the coefficient of kinetic friction between the furniture and the floor were doubled, what would happen to the acceleration of the system?

Accepted Answer

It would decrease

Question 12

Which equation correctly relates the net force on the gibbon at the lowest point of the swing?

Accepted Answer

$$T - mg = m\frac{v^2$}{r}$$

Question 13

A research rover is stationary on the equator of a rotating planet. Which of the following best describes the direction of the centripetal acceleration?

Accepted Answer

Toward the axis of rotation

Question 14

If the gibbon's speed at the lowest point of the swing were doubled, what would happen to the required upward force from the branch?

Accepted Answer

It would increase by a factor of four

Friction, Tension, and Kinematics: Bank Robbery Physics Problems

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