Q: A block of mass $$M$$ hangs at rest, supported by a rope that is fastened to the wall horizontally and has a tension $$T. $$The rope that is fastened to the ceiling makes an angle $$\theta$$ with the ceiling. What is the angle $$\theta$$?

$$\tan$$^{-1}$$\left(\frac{M}{T}\right)$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the formula for its maximum range on level ground?

$$\frac{v_0$^2 \sin 2\theta}{g}$$

Q: A block of mass $$m is $$sliding down an inclined plane of angle $$\theta$$ and coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block?

$$g(\sin \theta - \mu_k \cos \theta)$$

Question 1

A ball is thrown vertically upward with an initial velocity $$v_0. At $$the highest point of its trajectory, which of the following statements is correct?

Accepted Answer

The velocity is zero, the acceleration is directed downward, and the force of gravity acting on the ball is directed downward.

Question 2

A driver in a 1000 kg car traveling at 20 m/s slams on the brakes and skids to a stop. If the coefficient of friction between the tires and the horizontal road is $$\mu = 0.80$$, how long will the skid mark be?

Accepted Answer

$$16 	ext{ m}$$

Question 3

Three objects are connected by massless wires over a massless frictionless pulley as shown. The tension in the wire connecting the 10.0-kg and 15.0-kg objects is measured to be 133 N. What is the tension in A?

Accepted Answer

$$133 	ext{ N}$$

Question 4

A block of mass $$M$$ hangs at rest, supported by a rope that is fastened to the wall horizontally and has a tension $$T. $$The rope that is fastened to the ceiling makes an angle $$	heta$$ with the ceiling. What is the angle $$	heta$$?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{M}{T}ight)$$

Question 5

A car enters a 300-m-radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed at which the car can travel and thus curve without sliding?

Accepted Answer

$$42.5 	ext{ m/s}$$

Question 6

A small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface. If this object is moved 500 km farther from the planet, the gravitational force on it will be closest to:

Accepted Answer

$$71 	ext{ N}$$

Question 7

A satellite in a circular orbit of radius $$R$$ around planet $$X$$ has an orbital period $$T. If $$planet $$Y$$ had one-fourth as much mass, the orbital period of this satellite in an orbit of the same radius would be:

Accepted Answer

$$2T$$

Question 8

A block of mass $$m$$ slides down a frictionless incline of angle $$	heta. $$What is the acceleration of the block?

Accepted Answer

$$g \sin 	heta$$

Question 9

A skydiver of mass $$m$$ falls from a very high altitude. At what speed does she reach terminal velocity, given that the air resistance is proportional to the speed and is called drag force $$F = kv$$?

Accepted Answer

$$\frac{mg}{k}$$

Question 10

A block of mass $$M is $$suspended by two ropes, one attached horizontally to a wall and the other at an angle $$	heta to $$the ceiling. If the tension in the angled rope is $$T$$, what is the vertical component of the tension?

Accepted Answer

$$T \sin 	heta$$

Question 11

A 2-kg object moves in a circle of radius 0.5 m at a constant speed of 4 m/s. What is the magnitude of the centripetal force acting on the object?

Accepted Answer

$$32 	ext{ N}$$

Question 12

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its maximum range on level ground?

Accepted Answer

$$\frac{v_0$^2 \sin 2	heta}{g}$$

Question 13

A block of mass $$m is $$pulled across a horizontal surface with a force $$F at an $$angle $$	heta$$ above the horizontal. If the coefficient of kinetic friction is $$\mu_k$$, what is the frictional force acting on the block?

Accepted Answer

$$\mu_k (mg - F \sin 	heta)$$

Question 14

A roller coaster car of mass $$m$$ moves in a vertical circle of radius $$R at $$speed $$v. $$What is the normal force on the car at the top of the circle?

Accepted Answer

$$mg - \frac{mv^2$}{R}$$

Question 15

A block of mass $$m is at $$rest on a horizontal surface. A force $$F is $$applied horizontally. If the coefficient of static friction is $$\mu_s$$, what is the maximum value of $$F$$ before the block starts to move?

Accepted Answer

$$\mu_s mg$$

Question 16

A 5-kg object is dropped from a height of 20 m. Neglecting air resistance, what is its speed just before hitting the ground?

Accepted Answer

$$19.8 	ext{ m/s}$$

Question 17

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates on a frictionless surface. What is the period of oscillation?

Accepted Answer

$$2\pi \sqrt{\frac{m}{k}}$$

Question 18

A block of mass $$m is $$sliding down an inclined plane of angle $$	heta$$ and coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block?

Accepted Answer

$$g(\sin 	heta - \mu_k \cos 	heta)$$

Classical Mechanics: Forces, Motion, and Circular Dynamics Study Guide

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