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1. A small hoop of radius r = 0.1 m and mass m = 0.5 kg is released from rest at the top of a slope of height h = 0.4 m. The moment of inertia of a loop of mass m and radius r is mr^2. (Neglect air resistance). Assume g = 10 m/s^2. (14) (a) Find its speed when it reaches the bottom of the slope. (6) (b) Find its angular velocity when it reaches the bottom of the slope. 2. A mass m is attached to a horizontal spring of spring constant k and released at the turning point x = D. Neglect friction, air resistance and assume the motion is along the x-axis. Assume ? = ?(k/m) (6) (a) What is its speed at x = D/?2? (6) (b) Find x where the mass has the maximum acceleration? What is the acceleration? (6) (c) Find x where the mass has the maximum speed? What is the speed? 3. A uniform 5-m ladder weighs 100 N and leans against a frictionless vertical wall. The horizontal floor is rough enough that the foot of the ladder does not slide on the floor. Find (6) (a) Fn (6) (b) Ff (6) (c) fs. 4. Given c_water = 4186 J/kg·°C, c_Al = 900 J/kg·°C, c_ice = 2.00 × 10^3 J/kg·°C, latent heat of fusion for water is Lf = 33.5 × 10^4 J/kg. (24) (a) Pour 50 g of water at 60 °C into a 1.0 kg aluminum beaker whose temperature is 25 °C. What is the final temperature of the water and beaker at equilibrium. (extra credit 10 points) (b) Instead of pouring 50 g of water into the aluminum beaker, now suppose we drop a piece of ice (50 g) at -5 °C into the aluminum beaker whose temperature is 25 °C. What is the final temperature of the water and beaker at equilibrium. 5. A mass m1 = 2.0 kg at a height of 2.0 m slides down a frictionless slope from rest. It collides with mass m2 = 3.0 kg at the end of the slope. They stick together and slide a distance L on a rough horizontal surface before they stop. The kinetic friction coefficient ?k = 0.2 on the horizontal surface. Assume g = 10 m/s^2. (16) (a) Find the work done by the kinetic friction force on the horizontal surface. (4) (b) Find the distance L. (Extra credit problems) Use one or two sentences to explain the following. (2) (a) A figure skater spins faster when she draws in her arm. (8) (b) Children are often told not to stand too close to a rapidly moving train because they might get sucked under it.

          1. A small hoop of radius r = 0.1 m and mass m = 0.5 kg is released from rest at the top of a slope of height h = 0.4 m. The moment of inertia of a loop of mass m and radius r is mr^2. (Neglect air resistance). Assume g = 10 m/s^2.
(14) (a) Find its speed when it reaches the bottom of the slope.
(6) (b) Find its angular velocity when it reaches the bottom of the slope.

2. A mass m is attached to a horizontal spring of spring constant k and released at the turning point x = D. Neglect friction, air resistance and assume the motion is along the x-axis. Assume ? = ?(k/m)
(6) (a) What is its speed at x = D/?2?
(6) (b) Find x where the mass has the maximum acceleration? What is the acceleration?
(6) (c) Find x where the mass has the maximum speed? What is the speed?

3. A uniform 5-m ladder weighs 100 N and leans against a frictionless vertical wall. The horizontal floor is rough enough that the foot of the ladder does not slide on the floor. Find
(6) (a) Fn
(6) (b) Ff
(6) (c) fs.

4. Given c_water = 4186 J/kg·°C, c_Al = 900 J/kg·°C, c_ice = 2.00 × 10^3 J/kg·°C, latent heat of fusion for water is Lf = 33.5 × 10^4 J/kg.
(24) (a) Pour 50 g of water at 60 °C into a 1.0 kg aluminum beaker whose temperature is 25 °C. What is the final temperature of the water and beaker at equilibrium.
(extra credit 10 points) (b) Instead of pouring 50 g of water into the aluminum beaker, now suppose we drop a piece of ice (50 g) at -5 °C into the aluminum beaker whose temperature is 25 °C. What is the final temperature of the water and beaker at equilibrium.

5. A mass m1 = 2.0 kg at a height of 2.0 m slides down a frictionless slope from rest. It collides with mass m2 = 3.0 kg at the end of the slope. They stick together and slide a distance L on a rough horizontal surface before they stop. The kinetic friction coefficient ?k = 0.2 on the horizontal surface. Assume g = 10 m/s^2.
(16) (a) Find the work done by the kinetic friction force on the horizontal surface.
(4) (b) Find the distance L.

(Extra credit problems) Use one or two sentences to explain the following.
(2) (a) A figure skater spins faster when she draws in her arm.
(8) (b) Children are often told not to stand too close to a rapidly moving train because they might get sucked under it.

1. A small hoop of radius r = 0.1 m and mass m = 0.5 kg is released from rest at the top of a slope of height h = 0.4 m. The moment of inertia of a loop of mass m and radius r is mr^2. (Neglect air resistance). Assume g = 10 m/s^2.
(14) (a) Find its speed when it reaches the bottom of the slope.
(6) (b) Find its angular velocity when it reaches the bottom of the slope.

2. A mass m is attached to a horizontal spring of spring constant k and released at the turning point x = D. Neglect friction, air resistance and assume the motion is along the x-axis. Assume ? = ?(k/m)
(6) (a) What is its speed at x = D/?2?
(6) (b) Find x where the mass has the maximum acceleration? What is the acceleration?
(6) (c) Find x where the mass has the maximum speed? What is the speed?

3. A uniform 5-m ladder weighs 100 N and leans against a frictionless vertical wall. The horizontal floor is rough enough that the foot of the ladder does not slide on the floor. Find
(6) (a) Fn
(6) (b) Ff
(6) (c) fs.

4. Given cwater = 4186 J/kg·°C, cAl = 900 J/kg·°C, cice = 2.00 × 10^3 J/kg·°C, latent heat of fusion for water is Lf = 33.5 × 10^4 J/kg.
(24) (a) Pour 50 g of water at 60 °C into a 1.0 kg aluminum beaker whose temperature is 25 °C. What is the final temperature of the water and beaker at equilibrium.
(extra credit 10 points) (b) Instead of pouring 50 g of water into the aluminum beaker, now suppose we drop a piece of ice (50 g) at -5 °C into the aluminum beaker whose temperature is 25 °C. What is the final temperature of the water and beaker at equilibrium.

5. A mass m1 = 2.0 kg at a height of 2.0 m slides down a frictionless slope from rest. It collides with mass m2 = 3.0 kg at the end of the slope. They stick together and slide a distance L on a rough horizontal surface before they stop. The kinetic friction coefficient ?k = 0.2 on the horizontal surface. Assume g = 10 m/s^2.
(16) (a) Find the work done by the kinetic friction force on the horizontal surface.
(4) (b) Find the distance L.

(Extra credit problems) Use one or two sentences to explain the following.
(2) (a) A figure skater spins faster when she draws in her arm.
(8) (b) Children are often told not to stand too close to a rapidly moving train because they might get sucked under it.

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