**Physics 170. Midterm I**

**Please write your name at the top of the page**

**There are 4 problems. Each is assigned 25 points.**

Problem 1: 25 points

The speed of waves in the deep waters of the Pacific Ocean depends on the acceleration of gravity g, and on the wavelength of the waves (denoted ), which is measured in meters.

Use **dimensional
analysis** to find the dependence of the speed on g and .

Problem 2: 25 points

While standing on the edge of a 120 m high cliff, you throw a rock
**horizontally** at 14 m/s.

How far from the bottom of the cliff does it land (i.e. in the horizontal direction) ? Neglect air resistance.

Problem 3: 25 points

A roofer secures a 28-kg toolbox while working on a frictionless metal roof pitched at an angle of 40 . To do so, he uses a rope running horizontally as shown below.

a) Draw a diagram and show the forces which act on the toolbox.

b) What is the tension in the rope ?

Problem 4: 25 points

A 2.5 kg block is placed on a horizontal board, and the board is gradually tilted upwards (i.e. this is an inclined plane with an adjustable angle of inclination ). The block remains at rest until the board makes an angle of 38 to the horizontal at which point it begins to slide.

a) Draw a diagram which show the forces acting on the block.

b)
What is the coefficient of *static* friction between
the board and the surface of the 2.5 kg block ?

Wed Sep 3 13:59:28 HST 1997