Q: A car is driving around a flat curve of radius $$r. If $$the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed $$v_{\text{max}}$$ the car can have without skidding?

$$v_{\text{max}} = \sqrt{\mu_s g r}$$

Question 1

An astronaut weighs 99 N on the Moon, where the acceleration due to gravity is $$1.62\ \mathrm{m/s^2$}. $$How much does she weigh on Earth? (Assume $$g_{	ext{Earth}} = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

440 N

Question 2

A block is on a frictionless table on Earth. The block accelerates at $$5.3\ \mathrm{m/s^2$}$$ when a $$10\ \mathrm{N}$$ horizontal force is applied. The block and table are set up on the Moon ($$g = 1.62\ \mathrm{m/s^2$}). A $$horizontal force of $$5\ \mathrm{N} is $$now applied to the block on the Moon. What is the acceleration imparted to the block?

Accepted Answer

$$3.4\ \mathrm{m/s^2$}$$

Question 3

An object that weighs $$75\ \mathrm{N} is $$pulled on a horizontal surface by a horizontal pull of $$50\ \mathrm{N} to $$the right. The friction force on this object is $$30\ \mathrm{N} to $$the left. What is the acceleration of the object? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.6\ \mathrm{m/s^2$}$$

Question 4

A $$50.0\ \mathrm{kg}$$ crate is being pulled along a horizontal smooth surface. The pulling force is $$10.0\ \mathrm{N}$$ and is directed $$20.0^\circ$$ above the horizontal. What is the magnitude of the acceleration of the crate?

Accepted Answer

$$0.200\ \mathrm{m/s^2$}$$

Question 5

A $$10.0\ \mathrm{kg}$$ picture is held in place by two wires, the first one hanging at $$50.0^\circ to $$the left of the vertical and the second one at $$45.0^\circ to $$the right of the vertical. What is the tension in the first wire?

Accepted Answer

$$69.6\ \mathrm{N}$$

Question 6

A piano mover raises a $$1000\ \mathrm{N}$$ piano at a constant speed using a very light rope in a frictionless pulley system as shown. With what force is the mover pulling down on the rope?

Accepted Answer

$$500\ \mathrm{N}$$

Question 7

As shown, a $$10\ \mathrm{kg}$$ block on a perfectly smooth horizontal table is connected by a horizontal string to a $$63\ \mathrm{kg}$$ block that is hanging over the edge of the table. What is the magnitude of the acceleration of the $$10\ \mathrm{kg}$$ block when the other block is gently released? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$8.1\ \mathrm{m/s^2$}$$

Question 8

A $$5.0\ \mathrm{kg}$$ box slides on the surface of a ramp that rises at $$37^\circ$$ above the horizontal. The coefficient of kinetic friction between the box and the surface of the ramp is $$0.60. $$What is the magnitude of the acceleration of the box if it is sliding down the ramp? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$-2.1\ \mathrm{m/s^2$}$$

Question 9

The curved section of a horizontal highway is a circular unbanked arc of radius $$740\ \mathrm{m}. If $$the coefficient of static friction between this roadway and typical tires is $$0.40$$, what would be the maximum safe driving speed for this horizontal curved section of highway?

Accepted Answer

$$52\ \mathrm{m/s}$$

Question 10

A $$3.0\ \mathrm{kg}$$ package A is connected by a light string over a pulley to package B, which hangs vertically. Package A can slide along a rough plane inclined at $$30^\circ$$ above the horizontal. The coefficient of static friction between package A and the plane is $$0.40. $$What is the minimum mass that package B must have in order to start package A sliding up the ramp? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$3.6\ \mathrm{kg}$$

Question 11

A $$12\ \mathrm{kg}$$ block A is connected by a light rope over a frictionless pulley to an $$18\ \mathrm{kg}$$ block B, which is connected to block C by another rope. An external force $$P is $$applied downward on block A, causing block A to accelerate downward at $$2.5\ \mathrm{m/s^2$}. $$The tension in the rope connecting block B and block C is $$60\ \mathrm{N}. $$What is the mass of block C?

Accepted Answer

$$6.1\ \mathrm{kg}$$

Question 12

A car is driving around a flat curve of radius $$r. If $$the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed $$v_{	ext{max}}$$ the car can have without skidding?

Accepted Answer

$$v_{	ext{max}} = \sqrt{\mu_s g r}$$

Question 13

A $$10\ \mathrm{kg}$$ block is pulled across a horizontal surface with a force of $$40\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. The coefficient of kinetic friction is $$0.2. $$What is the acceleration of the block? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$1.8\ \mathrm{m/s^2$}$$

Question 14

A $$5.0\ \mathrm{kg}$$ box is sliding up a $$37^\circ$$ ramp with a coefficient of kinetic friction $$\mu_k = 0.60. $$What is the direction of the acceleration?

Accepted Answer

Down the ramp

Question 15

A $$20\ \mathrm{kg}$$ box is at rest on a horizontal surface. The coefficient of static friction is $$0.5. $$What is the minimum horizontal force required to start moving the box? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$100\ \mathrm{N}$$

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