Exam 4: Forces and Motion in Two and Three Dimensions

A 200-N block, on a 30 $\degree$ incline, is being held motionless by friction. The coefficient of static friction between the block and the plane is 0.60. The force due to friction is:

A mass is suspended from a string in an airplane. As the plane is in the process of taking off, it is found that the string, instead of being vertical, hangs at an angle of 13 $\degree$ from the vertical. What is the acceleration of the plane at this time?

A 15-kg block rests on a level, frictionless surface and is attached by a light string to a 10-kg hanging mass where the string passes over a massless frictionless pulley. If g = 9.8 m/s², what is the tension in the connecting string?

A sled is on a horizontal surface and a rope with tension T is pulling on it at an angle above the horizontal. The sled had mass M and does not move due to the frictional force. In this case the coefficient of friction is . In terms of the variables given and g, what is the magnitude of the frictional force in this case?

John throws a baseball from the outfield from shoulder height, at an initial velocity of 39.2 m/s at an initial angle of 30.0 $\degree$ with respect to the horizontal. The ball is in its trajectory for a total interval of 4.00 s before the third baseman catches it at an equal shoulder-height level. (Assume air resistance is negligible.) What is the ball's horizontal displacement?

A 100-kg box is placed on a ramp. As one end of the ramp is raised, the box begins to move downward just as the angle of inclination reaches 25 $\degree$ . What is the coefficient of static friction between box and ramp?

Plane A is flying at 600 mph in the northeast direction relative to the Earth. Plane B is flying at 500 mph in the north direction relative to the Earth. What is the direction of motion of Plane B as observed from Plane A?

A track star in the broad jump goes into the jump at 10 m/s and launches himself at 20 $\degree$ above the horizontal. How long is he in the air before returning to Earth? Note: g = 9.8 m/s².

A rifle is aimed horizontally toward the center of a target 71 m away. If the bullet strikes 10 cm below the center, what was the velocity of the bullet? Note: Ignore air friction.

A 150-N sled is pulled up a 28 $\degree$ slope at a constant speed by a force of 120 N. What is the coefficient of kinetic friction between sled and slope?

A baseball leaves the bat with a speed of 44.0 m/s and an angle of 30.0 $\degree$ above the horizontal. A 4.0-m high fence is located at a horizontal distance of 132 m from the point where the ball is struck. Assuming the ball leaves the bat 1.0 m above ground level, by how much does the ball clear the fence?

What is an inertial reference frame? It is one

A 200-N crate rests on a ramp; the maximum angle just before it slips is 21 $\degree$ with the horizontal. What is the coefficient of static friction between crate and ramp surfaces?

A 12-kg mass is placed on a 25.0 $\degree$ incline, and friction keeps it from sliding. The coefficient of static friction in this case is 0.580, and the coefficient of sliding friction is 0.520. What is the frictional force in this situation?

An Olympic skier moving at 22.0 m/s down a 30.0 $\degree$ slope encounters a region of wet snow, of coefficient of friction µ_k = 0.740. How far down the slope does she go before stopping?

A sled weighs 100 N. It is held in place on a frictionless 30 $\degree$ slope by a rope attached to a stake at the top; the rope is parallel to the slope. What is the normal force acting on the sled?

A mass is suspended from a string in an airplane. As the plane is in the process of taking off, it is found that the string, instead of being vertical, hangs at an angle from the vertical. What is the acceleration of the plane at this time?

A solid steel ball is dropped from a great height and when its speed reaches 20 m/s its acceleration downward is 7.35 m/s². What would be the terminal velocity in this situation?

A trapeze artist, with swing, weighs 700 N; he is momentarily held to one side by his partner so that the swing ropes make an angle of 30.0 $\degree$ with the vertical. In such a condition of static equilibrium, what is the horizontal force being applied by the partner?

A stone is thrown at an angle of 30 $\degree$ above the horizontal from the top edge of a cliff with an initial speed of 14 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 7.1 s. How far out from the cliff's edge does the stone travel horizontally? Note: g = 9.8 m/s² and air resistance is negligible.