Physics 170. Midterm I

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 ?

Tom Browder
Wed Sep 3 13:59:28 HST 1997