PHY-2048C – Fall 2020 SI with Camilo

Study Union Review

Disclaimer: This practice test does not necessarily cover all the material that is going to appear on the test, the questions are not the same as the actual test, and should not be used as the sole study guide for the test.

Topics:

2D Motion Forces Circular motion Energy and Work Linear momentum and conservation of momentum Rotational kinematics Angular momentum Simple harmonic motion Waves

1. A batter hits a baseball so that it leaves the bat at speed V 0 = 37m/s at and angle of 53.1 degrees.

a) Find the velocity (magnitude and direction) at t = 2 seconds

b) Find the time when the ball reaches its highest point and the height at this time

c) Find the horizontal distance that the ball travels as it hits the ground and the velocity right before impacting the ground.

c) Find the horizontal distance that the ball travels as it hits the ground and the velocity right before impacting the ground.

2. A box (m1) is on a 30-degree inclined ramp. This mass is connected by a string to another mass (m2) that is suspended over a massless and frictionless pulley. Mass 1 is 10 kg; Mass 2 is 30 kg. The coefficient of kinetic friction of Mass 1 and the inclined surface is 0.2.

a) Find the acceleration of the system. b) Find the tension in the rope.

3. A force of 130 N is applied to the front of a sled at an angle of 27.0 above the horizontal so as to pull the sled a distance of 170 meters. How much work was done by the applied force?

4. A block of mass m1 = 20.0 kg is connected to a block of mass m2 = 35.0 kg by a massless string that passes over a light, frictionless pulley. The 35.0-kg block is connected to a spring that has negligible mass and a force constant of k = 222 N/m as shown in the figure below. The spring is unstretched when the system is as shown in the figure, and the incline is frictionless. The 20.0-kg block is pulled a distance h = 25.0 cm down the incline of angle θ = 40.0 ◦ and released from rest. Find the speed of each block when the spring is again unstretched.

5. A 10.0kg block is released from rest at point A in the figure below. The track is frictionless except for the portion between points B and C, which has a length of 6.00 m. The block travels down the track, hits a spring of force constant 2 200 N/m, and compresses the spring 0.200 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and the rough surface between points B and C.

6. A satellite orbits Earth at an altitude of 400 kilometers above the planet’s surface.

(radius of earth = 6.38x106m)

a) What is its speed in meters per second?

b) What is the period of the satellite?

7. Two crates are sliding on a frictionless surface as shown in the figure below. The 11 kg crate is sliding to the right at 9.0 m/s and the 26 kg crate is sliding to the left at 6.0 m/s. The two crates collide and stick together. Use conservation of momentum to find the velocity of the two crates after the collision.

8. A 0.530-kg basketball hits a wall head-on with a forward speed of 18.0 m/s. It rebounds with a speed of 13.5 m/s. The contact time is 0.100 seconds. (a) determine the impulse with the wall, (b) determine the force of the wall on the ball.

9. Two masses are attached to a massless string that goes around a massive pulley as shown in the picture. Find an equation that gives the value of the acceleration of the system (a) in terms of m1, m2, M, and g.

10. Starting from rest, a 15-cm-diameter compact disk takes 4.0 s to reach an angular velocity of 3000 rpm. Assume that the angular acceleration is constant. The disk's moment of inertia 3x10-5kgm2.

a. How much torque is applied to the disk?

b. How many revolutions does it make before reaching full speed?

11. A classic physics demonstration involves firing a bullet into a block of wood suspended by strings from the ceiling. The height to which the wood rises below its lowest position is mathematically related to the pre-collision speed of the bullet. If a 9.7-gram bullet is fired into the center of a 1.1-kg block of wood and it rises upward a distance of 33 cm, then what was the pre-collision speed of the bullet?

12. A typical small rescue helicopter has four blades: Each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. 

(a) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm.

13. A 25-kg child stands at a distance r=1.0m from the axis of a rotating merry-go-round. The merry-go-round can be approximated as a uniform solid disk with a mass of 500 kg and a radius of 2.0 m. Find the moment of inertia of this system.(treat the child as a point mass)

14. Find the expression for the moment of inertia of a thin rod with length L if the axis of rotation is on the middle of the rod.

15. A uniform ladder is L=5.0m long and weighs 400.0 N. The ladder rests against a slippery vertical wall, as shown in the figure. The inclination angle between the ladder and the rough floor is β=53°. Find the reaction force from the wall on the ladder and the coefficient of static friction μs at the interface of the ladder with the floor that prevents the ladder from slipping.

16. A rod of length L = 1.0 m and mass M = 2 kg is hinged on one side so that it can rotate freely(imagine like a door but it is a rod). A bullet is then fired and hits the rod right at the edge. The bullet has mass m=5g and a speed of 200 m/s. What is the angular velocity of the rod with respect to the hinge just after the bullets embeds itself in the door?

17. A flywheel rotates without friction at an angular velocity ω_0=600rev/min on a frictionless, vertical shaft of negligible rotational inertia. A second flywheel, which is at rest and has a moment of inertia three times that of the rotating flywheel, is dropped onto it. Because friction exists between the surfaces, the flywheels very quickly reach the same rotational velocity, after which they spin together. (a) Use the law of conservation of angular momentum to determine the angular velocity ω of the combination.

18. Consider a 550 g ball hanging on a spring with a spring constant equal to 22 N/m. We pull down on the ball and let it go, so that it oscillates up and down. Find:

(a) The period of the oscillation.

(b) The frequency of the oscillation.

19. A transverse mechanical wave propagates in the positive x-direction through a spring with a constant wave speed, and the medium oscillates between +A and −A around an equilibrium position. The graph in Figure 16.6 shows the height of the spring (y) versus the position (x), where the x-axis points in the direction of propagation. The figure shows the height of the spring versus the x-position at t=0.00s as a dotted line and the wave at t=3.00s as a solid line. Assume the wave has not traveled more than 1 wavelength in this time. (a) Determine the wavelength and amplitude of the wave. (b) Find the propagation velocity of the wave. (c) Calculate the period and frequency of the wave.

20) A transverse wave on a taut string is modeled with the wave function:

y(x,t)=(0.2m)*sin(6.28m−1x−1.57s−1t).

Find the amplitude, wavelength, period, and speed of the wave.