True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 114. The exam period was 90 minutes; the mean score was 93.2; the median score was 95. Click here to see the formula sheet that came with the exam.

A car undergoing uniform acceleration, a = 4 m/s^{2}, is travelling at a velocity of 40 m/s as it enters a tunnel. When the car exits the tunnel, its velocity is 72 m/s.

How long is the tunnel?

(a) 7 m (b) 90 m (c) 197 m (d) 378 m (e) 448 m

(a) 0.2 s (b) 1.0 s (c) 4.1 s (d) 7.0 s (e) 8.0 s

(a) closer to V_{in} than V_{out}. (b) half way between V_{in} and V_{out}. (c) closer to V_{out} than V_{in}.

Mr. Stick lives on the planet Teflon where the force due to gravity is different than that of Earth. Mr. Stick drops a small water balloon off the top of a building (V_{0} = 0 m/s). He releases the balloon at a height H = 10 m above the surface of Teflon. The balloon hits the ground 1.8 seconds after it is dropped and has a velocity V_{1} on impact. (Neglect Teflonian air resistance.)

What is the acceleration due to gravity on the planet Teflon?

(a) 3.5 m/s^{2} (b) 6.2 m/s^{2} (c) 8.3 m/s^{2} (d) 9.8 m/s^{2} (e) 11.6 m/s^{2}

(a) V_{2} > V_{1} (b) V_{2} = V_{1} (c) V_{2} < V_{1}

The two massless springs have the same length L_{0} when not compressed or stretched. The stiffness of each spring is k_{1} and k_{2}, respectively. Mass M_{1} hangs from spring 1 and it reaches equilibrium at position L_{1}. Mass M_{2} hangs from spring 2 and it reaches equilibrium at position L_{2}.

If k_{2} = 2 k_{1} and M_{2} = 2 M_{1}, which one of the relationships below is correct?

(a) L_{2} = 2 L_{1} (b) L_{1} = 2 L_{2} (c) L_{1} = L_{2} (d) L_{2} = 4 L_{1} (e) L_{1} = 4 L_{2}

(a) L_{2} = 3 L_{1} (b) L_{1} = 3 L_{2} (c) L_{2} = 2 L_{1} - 3 L_{0} (d) L_{2} = 3 L_{1} - 2 L_{0} (e) L_{1} = 3 (L_{2} - L_{0})

A mass m = 7.1 kg is hung over a massless pulley. Two masses, each with mass M = 15.3 kg are attached to m with a massless rope as shown in the drawing below. The desktop and the pulley are frictionless.

The tension T_{1} is greater than the tension T_{2}.

(T) True (F) False

(a) T_{2} > T_{3} (b) T_{2} = T_{3} (c) T_{2} < T_{3}

(a) a = 0.0835 m/s^{2} (b) a = 1.40 m/s^{2} (c) a = 1.85 m/s^{2} (d) a = 5.69 m/s^{2} (e) a = 10.42 m/s^{2}

A mass m is tied to a string of length R = 0.5 m and set in uniform circular motion in the vertical plane, as shown in the left figure. The angular velocity of the motion is ω = 3.1 rad/s.

The string tension is largest at

(a) the top of the circle. (b) the bottom of the circle. (c) it is the same at all points on the circle.

(a) 0.10 m (b) 0.25 m (c) 0.31 m (d) 0.38 m (e) 0.49 m

Block m_{1} (3 kg) is hanging over the edge of a table and is attached to block m_{2} (17 kg) by a massless string that runs over a frictionless pulley as shown in the figure. The table has static and kinetic coefficients of friction of 0.35 and 0.2 respectively. Block m_{2} is also attached to a wall by an ideal, massless spring with a spring constant of 100 N/m.

The force of m_{1} on the earth is equal in magnitude to the force of the earth on m_{1}.

(a) 0.0 m (b) 0.075 m (c) 0.121 m (d) 0.152 m (e) 0.289 m

A tennis ball of weight W = 0.5 N is attached to a rope and swung in a vertical circle. The rope is L = 1 m in length. When the ball is at its highest point, the tension in the rope is measured to be zero.

What is the tangential velocity of the ball at its highest point?

(a) 3.1 m/s (b) 4.4 m/s (c) 8.8 m/s (d) 19.6 m/s (e) 79.3 m/s

(a) W (b) W (1+v^{2}/gL) (c) W(1-v^{2}/gL)

A student is walking in a straight line along Green St. at a constant velocity of 2 m/s. She tosses a pen into the air at an angle of 60° with respect to the vertical in her reference frame. A stationary observer on the other side of the street (directly across from her) observes that the pen goes straight up vertically and then falls to the ground. Assume the student is walking in the positive x-direction.

As measured by the student who tossed the pen, what is the x-component of the velocity of the pen?

(a) v_{x,s} = -4 m/s (b) v_{x,s} = -2 m/s (c) v_{x,s} = 0 m/s (d) v_{x,s} = +2 m/s, (e) v_{x,s} = +4 m/s

(a) v_{x,o} = -2 m/s (b) v_{x,o} = 0 m/s (c) v_{x,o} = +2 m/s

(a) (b) (c) (d) (e)

A space telescope of mass m_{t} = 10,000 kg is in a stable orbit above the Earth at an altitude h = 3630 km. The radius and mass of the Earth are R_{E} = 6370 km and M_{E} = 6 × 10^{24} kg, respectively. Newton's gravitational constant is G = 6.672 × 10^{-11} N m^{2}/kg^{2}.

Once in orbit, what is the force of gravitational attraction between the space telescope and the Earth?

(a) 0 N (b) 800 N (c) 5,000 N (d) 30,000 N (e) 40,000 N

(a) (b) (c)

(a) M (g+a) (b) M (g-a) (c) 2 M (g+a)

A block of mass M = 13.4 kg is supported on a frictionless ramp by a spring having a constant k = 145 N/m. When the ramp is horizontal, as in view a) below, the equilibrium position of the mass is at x = 0. The angle of the ramp is then changed to 25°, as in view b) below.

What is the new equilibrium position of the block, x_{1}?

(a) 0.12 m (b) 0.19 m (c) 0.38 m (d) 0.41 m (e) 0.56 m

(a) 17.6 N (b) 31.4 N (c) 44.7 N (d) 59.2 N (e) 125.6 N