Linear Momentum and Rotational Motion

Please solve the following problems. You must show all work.

- A rail car of mass 4500 kg is moving with a velocity of 12.4 m/s collides with a stationary rail car of mass 6700 kg. What is the velocity of the two cars if they stick after they collide?
- A tennis player hits a 1.45 kg tennis ball with a racket of mass 2.5 kg. If he hits the ball with a velocity of 7.5 m/s and then stops, what impulse did he imply on the ball? What is the ball’s velocity?
- A 35 g bullet is fired in a ballistic pendulum device (see page 178 In text) and increases the height of the center of mass of the device and the bullet by 2.1 cm. If the level arm has a mass of 3.4 kg, what was the initial velocity of the bullet?
- A puck slides on a surface for 5.6 m before it stops. If it was moving at a velocity of 15 m/s and has a mass of 1.2 kg, what is the force of friction exerted on the puck? There is a non-conservative work done on the puck equal to the change in kinetic energy, or:
- If a tire on a semi-truck is 1.1 m. How many FULL rotations will the tire roll if the truck moves 24.5 meters?
- A large circus ride has a centripetal acceleration at 6.0 m/s2. If the circular ride has a radius of 11.0 m, what is its velocity at the edge?
- If a 56 diameter circular disk is uniformly angularly accelerating at a rate of 5.0 rad/s2, what will the final angular velocity be after 4.0 seconds if it starts at a rate of 10.0 rad/s? What angle is subtended over that time?
- A 40.0 N force is applied to a 46.0 cm long torque wrench. What is the net torque applied to the nut? Also if this force is applied for 3.0 seconds and the bolt starts from rest and ends with an angular velocity of 0.5 rad/s, what is the bolt’s moment of inertia?

** Notes on homework: **

On number 2, it means the racket stops after it strikes the ball.

On number 3, it refers to page 178, but it really means example 7-9 on page 181.

For the second part of number 4, it sounds confusing, but it’s asking about the momentum of the puck.

Number 5 is referring to the DIAMETER of the tire. If it meant the radius, the tire would over 7 feet tall.

Answer the second part of number 7 in radians or revolutions. Don’t use degrees. With these rotational problems, you should get used to putting your calculator in Radian mode.

On number 8, you can assume the force is being applied perpendicular to the wrench.

**A rail car of mass 4500 kg is moving with a velocity of 12.4 m/s collides with a stationary rail car of mass 6700 kg. What is the velocity of the two cars if they stick after they collide?**

Step 1 – work out the total momentum before the event (before the collision):

p = m × v

• Momentum of carriage A before = 4,500 × 12.4 = 55,800 kg m/s

• Momentum of carriage B before = 6,700 × 0 = 0 kg m/s

• Total momentum before = 55,800 + 0 = 55,800 kg m/s.

Step 2 – work out the total momentum after the event (after the collision):

• Because momentum is conserved, total momentum afterwards = 55,800 kg m/s

Step 3 – work out the total mass after the event (after the collision):

• Total mass = mass of carriage A + mass of carriage B = 4,500 + 6,700 = 11,200 kg

Step 4 – work out new velocity:

p = m × v … so … v = p ÷ m

• Velocity (after the collision) = 55,800 ÷ 11,200 = 4.982 m/s

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